VOLUME 82 NUMBER 284 OCTOBER 2013

A M E R I C A N M A T H E M A T I C A L S O C I E T Y

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MATHEMATICS OF COMPUTATION

CONTENTS

Vol. 82, No. 284 October 2013

Alexey Chernov and Christoph Schwab, First order k-th moment finiteelement analysis of nonlinear operator equations with stochastic data 1859

Qiang Du, Lili Ju, Li Tian, and Kun Zhou, A posteriori error analysisof finite element method for linear nonlocal diffusion and peridynamicmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1889

Tan Bui-Thanh, Leszek Demkowicz, and Omar Ghattas, Construc-tively well-posed approximation methods with unity inf–sup and conti-nuity constants for partial differential equations . . . . . . . . . . . . . . . . . . . . . . 1923

Ross Ingram, A new linearly extrapolated Crank-Nicolson time-steppingscheme for the Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1953

Eskil Hansen and Tony Stillfjord, Convergence of the implicit-explicitEuler scheme applied to perturbed dissipative evolution equations . . . . 1975

Kassem Mustapha, A Superconvergent discontinuous Galerkin method forVolterra integro-differential equations, smooth and non-smooth kernels 1987

Froilan M. Dopico, Vadim Olshevsky, and Pavel Zhlobich, Stabilityof QR-based fast system solvers for a subclass of quasiseparable rankone matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2007

Carl Jagels and Lothar Reichel, The structure of matrices in rationalGauss quadrature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2035

Yi Yang, Michael Moller, and Stanley Osher, A dual split Bregmanmethod for fast `1 minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2061

Xudong Yao, A minimax method for finding saddle critical points of uppersemi-differentiable locally Lipschitz continuous functional in Hilbertspace and its convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2087

Christine Choirat and Raffaello Seri, Computational aspects of Cui-Freeden statistics for equidistribution on the sphere . . . . . . . . . . . . . . . . . . 2137

Nabi Chegini, Stephan Dahlke, Ulrich Friedrich, and RobStevenson, Piecewise tensor product wavelet bases by extensions andapproximation rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2157

C. Ortner and A. V. Shapeev, Analysis of an energy-basedatomistic/continuum approximation of a vacancy in the 2D triangularlattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2191

Ana Romero and Julio Rubio, Homotopy groups of suspended classifyingspaces: An experimental approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2237

Claude-Pierre Jeannerod, Nicolas Louvet, and Jean-Michel Muller,Further analysis of Kahan’s algorithm for the accurate computation of2 × 2 determinants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2245

Mark W. Coffey and George Csordas, On the log-concavity of a Jacobitheta function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2265

Georges Klein, An extension of the Floater–Hormann family of barycentricrational interpolants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2273

A. Papageorgiou, I. Petras, J. F. Traub, and C. Zhang, A fastalgorithm for approximating the ground state energy on a quantumcomputer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2293

Michael Strauss, The second order spectrum and optimal convergence . . . 2305

A. Bayad and J. Chikhi, Mobius inversion formulae for Apostol-Bernoullitype polynomials and numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2327

Tianxin Cai and Deyi Chen, A new variant of the Hilbert-Waringproblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2333

Anna Morra, An algorithm to compute relative cubic fields . . . . . . . . . . . . . . 2343

Werner Bley and Ruben Debeerst, Algorithmic proof of the epsilonconstant conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2363

Robert Granger and Andrew Moss, Generalised Mersenne numbersrevisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2389

Murray R. Bremner and Jiaxiong Hu, Fundamental invariants for theaction of SL3(C) × SL3(C) × SL3(C) on 3 × 3 × 3 arrays . . . . . . . . . . . . 2421

Kevin Broughan, Sergio Guzman Sanchez, and Florian Luca, Perfectrepdigits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2439

INDEX TO VOLUME 82 (2013)

Akrivis, Georgios. Implicit–explicit multistep methods for nonlinear parabolic equations, 45

Antonietti, Paola F., Lourenco Beirao da Veiga, and Marco Verani. A mimetic discretization ofelliptic obstacle problems, 1379

Antonopoulos, D. C., and V. A. Dougalis. Error estimates for Galerkin approximations of the

“classical” Boussinesq system, 689Area, Ivan, Dimitar K. Dimitrov, Eduardo Godoy, and Vanessa G. Paschoa. Zeros of classical

orthogonal polynomials of a discrete variable, 1069

Bao, Weizhu, and Yongyong Cai. Optimal error estimates of finite difference methods for theGross-Pitaevskii equation with angular momentum rotation, 99

Bayad, A., and J. Chikhi. Mobius inversion formulae for Apostol-Bernoulli type polynomials

and numbers, 2327Benning, Martin. See Burger, Martin

Ben-yu, Guo, Sun Tao, and Zhang Chao. Jacobi and Laguerre quasi-orthogonal approximations

and related interpolations, 413Bernstein, Daniel J., Peter Birkner, Tanja Lange, and Christiane Peters. ECM using Edwards

curves, 1139Berthon, Christophe, Philippe G. LeFloch, and Rodolphe Turpault. Late-time/stiff-relaxation

asymptotic-preserving approximations of hyperbolic equations, 831

Bidwell, S., M. E. Hassell, and C. R. Westphal. A weighted least squares finite element methodfor elliptic problems with degenerate and singular coefficients, 673

Birkner, Peter. See Bernstein, Daniel J.

Blanes, S., F. Casas, P. Chartier, and A. Murua. Optimized high-order splitting methods forsome classes of parabolic equations, 1559

Bley, Werner, and Ruben Debeerst. Algorithmic proof of the epsilon constant conjecture, 2363

Bollobas, Bela, Malte Lackmann, and Dierk Schleicher. A small probabilistic universal set ofstarting points for finding roots of complex polynomials by Newton’s method, 443

Bona, J. L., H. Chen, O. Karakashian, and Y. Xing. Conservative, discontinuous Galerkin–

methods for the generalized Korteweg–de Vries equation, 1401Bremner, Murray R., and Jiaxiong Hu. Fundamental invariants for the action of SL3(C) ×

SL3(C)× SL3(C) on 3× 3× 3 arrays, 2421Broughan, Kevin, Sergio Guzman Sanchez, and Florian Luca. Perfect repdigits, 2439

Bruin, Peter. Computing in Picard groups of projective curves over finite fields, 1711

Bui-Thanh, Tan, Leszek Demkowicz, and Omar Ghattas. Constructively well-posed approxima-tion methods with unity inf–sup and continuity constants for partial differential equations,

1923

Burger, Martin, Michael Moller, Martin Benning, and Stanley Osher. An adaptive inverse scalespace method for compressed sensing, 269

Cai, Tianxin. See Zhang, YongCai, Tianxin, and Deyi Chen. A new variant of the Hilbert-Waring problem, 2333Cai, Yongyong. See Bao, Weizhu

Caley, Timothy. The Prouhet-Tarry-Escott problem for Gaussian integers, 1121

Carmelo, Emerson L. Monte. See Martinhao, Anderson N.Casas, F. See Blanes, S.

Castillo, Kenier, and Francisco Marcellan. Generators of rational spectral transformations fornontrivial C-functions, 1057

Chao, Zhang. See Ben-yu, Guo

Chartier, P. See Blanes, S.Chegini, Nabi, Stephan Dahlke, Ulrich Friedrich, and Rob Stevenson. Piecewise tensor product

wavelet bases by extensions and approximation rates, 2157

Chen, Chuanmiao, and Shufang Hu. The highest order superconvergence for bi-k degree rectan-gular elements at nodes: A proof of 2k-conjecture, 1337

Chen, Deyi. See Cai, Tianxin

Chen, H. See Bona, J. L.Chenoweth, Samuel K. M., Julio Soria, and Andrew Ooi. An improved interpolation scheme for

finite volume simulations on unstructured meshes, 803Chernov, Alexey, and Christoph Schwab. First order k-th moment finite element analysis of

nonlinear operator equations with stochastic data, 1859

INDEX TO VOLUME 82 (2013)

Cheze, Guillaume. A recombination algorithm for the decomposition of multivariate rational

functions, 1793

Chikhi, J. See Bayad, A.Choirat, Christine, and Raffaello Seri. Computational aspects of Cui-Freeden statistics for equidis-

tribution on the sphere, 2137

Cifani, Simone, and Espen R. Jakobsen. On the spectral vanishing viscosity method for periodicfractional conservation laws, 1489

Cockburn, Bernardo, Ivan Merev, and Jianliang Qian. Local a posteriori error estimates for

time-dependent Hamilton-Jacobi equations, 187Cockburn, Bernardo, and Ke Shi. Conditions for superconvergence of HDG methods for Stokes

flow, 651

Coffey, Mark W., and George Csordas. On the log-concavity of a Jacobi theta function, 2265Cohen, Elaine, Tom Lyche, and Richard F. Riesenfeld. A B-spline-like basis for the Powell-Sabin

12-split based on simplex splines, 1667Csordas, George. See Coffey, Mark W.

Cvetkovic-Ilic, Dragana S. See Liu, Xiaoji

Dahlke, Stephan. See Chegini, NabiDaubechies, I. See Lipman, Y.

Debeerst, Ruben. See Bley, Werner

Debrabant, Kristian, and Espen R. Jakobsen. Semi-Lagrangian schemes for linear and fullynon-linear diffusion equations, 1433

Delgado, M., J. I. Farran, P. A. Garcıa-Sanchez, and D. Llena. On the generalized Feng-Rao

numbers of numerical semigroups generated by intervals, 1813Demkowicz, Leszek. See Bui-Thanh, Tan

Demlow, Alan, and Stig Larsson. Local pointwise a posteriori gradient error bounds for the

Stokes equations, 625Dick, Alexander, Othmar Koch, Roswitha Marz, and Ewa Weinmuller. Convergence of collo-

cation schemes for boundary value problems in nonlinear index 1 DAEs with a singularpoint, 893

Dimitrov, Dimitar K. See Area, Ivan

Dong, Bin. See Zhang, YongDopico, Froilan M., Vadim Olshevsky, and Pavel Zhlobich. Stability of QR-based fast system

solvers for a subclass of quasiseparable rank one matrices, 2007

Dougalis, V. A. See Antonopoulos, D. C.Dragunov, D. V. See Makarov, V. L.

Du, Qiang, Lili Ju, Li Tian, and Kun Zhou. A posteriori error analysis of finite element method

for linear nonlocal diffusion and peridynamic models, 1889Dziuk, Gerhard, and Charles M. Elliott. L2-estimates for the evolving surface finite element

method, 1Elliott, Charles M. See Dziuk, GerhardFarashahi, Reza R., Pierre-Alain Fouque, Igor E. Shparlinski, Mehdi Tibouchi, and J. Felipe

Voloch. Indifferentiable deterministic hashing to elliptic and hyperelliptic curves, 491Farran, J. I. See Delgado, M.

Feng, Xiaobing, and Yulong Xing. Absolutely stable local discontinuous Galerkin methods for

the Helmholtz equation with large wave number, 1269Fouque, Pierre-Alain. See Farashahi, Reza R.

Friedrich, Ulrich. See Chegini, Nabi

Galbraith, Steven D., John M. Pollard, and Raminder S. Ruprai. Computing discrete logarithmsin an interval, 1181

Gao, Hao, and Hongkai Zhao. Analysis of a numerical solver for radiative transport equation,

153Garcıa-Sanchez, P. A. See Delgado, M.

Ghattas, Omar. See Bui-Thanh, Tan

Gittelson, Claude Jeffrey. An adaptive stochastic Galerkin method for random elliptic operators,1515

Godoy, Eduardo. See Area, IvanGong, Wei. Error estimates for finite element approximations of parabolic equations with mea-

sure data, 69

INDEX TO VOLUME 82 (2013)

Granger, Robert, and Andrew Moss. Generalised Mersenne numbers revisited, 2389

Griebel, Michael, and Helmut Harbrecht. On the construction of sparse tensor product spaces,

975Griebel, Michael, Frances Y. Kuo, and Ian H. Sloan. The smoothing effect of integration in Rd

and the ANOVA decomposition, 383

Guitart, Xavier, and Marc Masdeu. Continued fractions in 2-stage Euclidean quadratic fields,1223

Hakberg, Bengt. A discrete KPP-theory for Fisher’s equation, 781

Han, Bin, and Xiaosheng Zhuang. Algorithms for matrix extension and orthogonal wavelet filterbanks over algebraic number fields, 459

Han, Houde, and Zhongyi Huang. Tailored finite point method based on exponential bases for

convection-diffusion-reaction equation, 213Hansen, Eskil, and Tony Stillfjord. Convergence of the implicit-explicit Euler scheme applied to

perturbed dissipative evolution equations, 1975Harbrecht, Helmut. See Griebel, Michael

Hare, Kevin G., and Maysum Panju. Some comments on Garsia numbers, 1197

Hassell, M. E. See Bidwell, S.Hiptmair, Ralf, Andrea Moiola, and Ilaria Perugia. Error analysis of Trefftz-discontinuous Galerkin

methods for the time-harmonic Maxwell equations, 247

Hirn, Adrian. Finite element approximation of singular power-law systems, 1247Holden, Helge, Kenneth H. Karlsen, and Trygve Karper. Operator splitting for two-dimensional

incompressible fluid equations, 719

Holden, Helge, Christian Lubich, and Nils Henrik Risebro. Operator splitting for partial differ-ential equations with Burgers nonlinearity, 173

Hu, Jiaxiong. See Bremner, Murray R.

Hu, Shufang. See Chen, ChuanmiaoHuang, Jingfang. See Jiang, Shidong

Huang, Zhongyi. See Han, HoudeIliescu, Traian, and Zhu Wang. Variational multiscale proper orthogonal decomposition: Convection-

dominated convection-diffusion-reaction equations, 1357

Ingram, Ross. A new linearly extrapolated Crank-Nicolson time-stepping scheme for the Navier-Stokes equations, 1953

Ionica, Sorina, and Antoine Joux. Pairing the volcano, 581

Jagels, Carl, and Lothar Reichel. The structure of matrices in rational Gauss quadrature, 2035Jakobsen, Espen R. See Cifani, Simone

. See Debrabant, Kristian

Jeannerod, Claude-Pierre, Nicolas Louvet, and Jean-Michel Muller. Further analysis of Kahan’salgorithm for the accurate computation of 2× 2 determinants, 2245

Jiang, Shidong, Zhi Liang, and Jingfang Huang. A fast algorithm for Brownian dynamics sim-ulation with hydrodynamic interactions, 1631

Jin, Qinian. Further convergence results on the general iteratively regularized Gauss-Newton

methods under the discrepancy principle, 1647Jin, Shi, Jian-guo Liu, and Li Wang. A domain decomposition method for semilinear hyperbolic

systems with two-scale relaxations, 749

Joux, Antoine. See Ionica, SorinaJu, Lili. See Du, Qiang

Karabina, Koray. Squaring in cyclotomic subgroups, 555

Karakashian, O. See Bona, J. L.Karlsen, Kenneth H. See Holden, Helge

Karper, Trygve. See Holden, Helge

Kinoshita, Takehiko. See Watanabe, YoshitakaKlein, Georges. An extension of the Floater–Hormann family of barycentric rational interpolants

, 2273Klimenko, Ya. V. See Makarov, V. L.

Koch, Othmar. See Dick, Alexander

Koumandos, Stamatis, and Martin Lamprecht. Complete monotonicity and related properties ofsome special functions, 1097

INDEX TO VOLUME 82 (2013)

Krylov, N. V. Interior estimates for second-order differences of solutions of finite-difference

elliptic Bellman’s equations, 1463

Kuo, Frances Y. See Griebel, MichaelLackmann, Malte. See Bollobas, Bela

Lamprecht, Martin. See Koumandos, Stamatis

Lange, Tanja. See Bernstein, Daniel J.Larsson, Stig. See Demlow, Alan

LeFloch, Philippe G. See Berthon, Christophe

Liang, Zhi. See Jiang, ShidongLipman, Y., J. Puente, and I. Daubechies. Conformal Wasserstein distance: II. computational

aspects and extensions, 331

Liu, Hailiang, Olof Runborg, and Nicolay M. Tanushev. Error estimates for Gaussian beamsuperpositions, 919

Liu, Jian-guo. See Jin, ShiLiu, Xiaoji, Shuxia Wu, and Dragana S. Cvetkovic-Ilic. New results on reverse order law for

{1, 2, 3}- and {1, 2, 4}-inverses of bounded operators, 1597

Liu, Youming, and Junjian Zhao. An extension of Bittner and Urban’s theorem, 401Llena, D. See Delgado, M.

Louvet, Nicolas. See Jeannerod, Claude-Pierre

Lu, Shuai, and Peter Mathe. Heuristic parameter selection based on functional minimization:Optimality and model function approach, 1609

Lu, Zhaosong. See Zhang, Yong

Lubich, Christian. See Holden, HelgeLuca, Florian. See Broughan, Kevin

Lyche, Tom. See Cohen, Elaine

Makarov, V. L., D. V. Dragunov, and Ya. V. Klimenko. The FD-method for solving Sturm-Liouville problems with special singular differential operator, 953

Marcellan, Francisco. See Castillo, KenierMartinhao, Anderson N., and Emerson L. Monte Carmelo. Short covering codes arising from

matchings in weighted graphs, 605

Marz, Roswitha. See Dick, AlexanderMasdeu, Marc. See Guitart, Xavier

Mathe, Peter. See Lu, Shuai

Melquiond, Guillaume, W. Georg Nowak, and Paul Zimmermann. Numerical approximation ofThe Masser-Gramain constant to four decimal digits: δ = 1.819..., 1235

Merev, Ivan. See Cockburn, Bernardo

Miller, Robert L., and Michael Stoll. Explicit isogeny descent on elliptic curves, 513Moiola, Andrea. See Hiptmair, Ralf

Molchanov, Vladimir, and Marcel Oliver. Convergence of the Hamiltonian particle-mesh methodfor barotropic fluid flow, 861

Moller, Michael. See Burger, Martin. See Yang, Yi

Morra, Anna. An algorithm to compute relative cubic fields, 2343

Moss, Andrew. See Granger, Robert

Muller, Jean-Michel. See Jeannerod, Claude-PierreMurua, A. See Blanes, S.

Mustapha, Kassem. A Superconvergent discontinuous Galerkin method for Volterra integro-

differential equations, smooth and non-smooth kernels, 1987Nakao, Mitsuhiro T. See Watanabe, Yoshitaka

Nielsen, Johan Sejr Brinch, and Jakob Grue Simonsen. An experimental investigation of the

normality of irrational algebraic numbers, 1837Nowak, W. Georg. See Melquiond, Guillaume

Oliver, Marcel. See Molchanov, VladimirOlshevsky, Vadim. See Dopico, Froilan M.

Ooi, Andrew. See Chenoweth, Samuel K. M.

Ortner, C., and A. V. Shapeev. Analysis of an energy-based atomistic/continuum approximationof a vacancy in the 2D triangular lattice, 2191

Osher, Stanley. See Burger, Martin

INDEX TO VOLUME 82 (2013)

. See Yang, Yi

Pani, Amiya K. See Yadav, Sangita

Panju, Maysum. See Hare, Kevin G.Papageorgiou, A., I. Petras, J. F. Traub, and C. Zhang. A fast algorithm for approximating the

ground state energy on a quantum computer, 2293

Park, Eun-Jae. See Yadav, SangitaPaschoa, Vanessa G. See Area, Ivan

Perugia, Ilaria. See Hiptmair, Ralf

Peters, Christiane. See Bernstein, Daniel J.Petras, I. See Papageorgiou, A.

Pollard, John M. See Galbraith, Steven D.

Puente, J. See Lipman, Y.Qian, Jianliang. See Cockburn, Bernardo

Reichel, Lothar. See Jagels, CarlRiesenfeld, Richard F. See Cohen, Elaine

Risebro, Nils Henrik. See Holden, Helge

Romero, Ana, and Julio Rubio. Homotopy groups of suspended classifying spaces: An experi-mental approach, 2237

Rubio, Julio. See Romero, Ana

Runborg, Olof. See Liu, HailiangRuprai, Raminder S. See Galbraith, Steven D.

Sanchez, Sergio Guzman. See Broughan, Kevin

Schleicher, Dierk. See Bollobas, BelaSchwab, Christoph. See Chernov, Alexey

Seri, Raffaello. See Choirat, Christine

Sfakianakis, Nikolaos. Adaptive mesh reconstruction for hyperbolic conservation laws with totalvariation bound, 129

Shapeev, A. V. See Ortner, C.Shi, Ke. See Cockburn, Bernardo

Shibuta, Takafumi. Irreducibility criterion for algebroid curves, 531

Shparlinski, Igor E. See Farashahi, Reza R.Simonsen, Jakob Grue. See Nielsen, Johan Sejr Brinch

Sloan, Ian H. See Griebel, Michael

Soria, Julio. See Chenoweth, Samuel K. M.Spalevic, Miodrag M. Error bounds of Gaussian quadrature formulae for one class of Bernstein-

Szego weights, 1037

Stein, William, and Christian Wuthrich. Algorithms for the arithmetic of elliptic curves usingIwasawa theory, 1757

Stevenson, Rob. See Chegini, NabiStillfjord, Tony. See Hansen, EskilStoll, Michael. See Miller, Robert L.

Strauss, Michael. The second order spectrum and optimal convergence, 2305Szmytkowski, Rados law. Erratum to “Formulas and Theorems for the Special Functions of

Mathematical Physics” by W. Magnus, F. Oberhettinger, R. P. Soni, 1709

Tanushev, Nicolay M. See Liu, HailiangTao, Sun. See Ben-yu, Guo

Tian, Li. See Du, Qiang

Tibouchi, Mehdi. See Farashahi, Reza R.Traub, J. F. See Papageorgiou, A.

Turpault, Rodolphe. See Berthon, Christophe

da Veiga, Lourenco Beirao. See Antonietti, Paola F.Verani, Marco. See Antonietti, Paola F.

Voloch, J. Felipe. See Farashahi, Reza R.

Wang, Li. See Jin, ShiWang, Li-Lian. See Xie, Ziqing

Wang, Ming, and Jinchao Xu. Minimal finite element spaces for 2m-th-order partial differentialequations in Rn, 25

Wang, Zhu. See Iliescu, Traian

INDEX TO VOLUME 82 (2013)

Watanabe, Yoshitaka, Takehiko Kinoshita, and Mitsuhiro T. Nakao. A posteriori estimates of in-

verse operators for boundary value problems in linear elliptic partial differential equations,

1543Weinmuller, Ewa. See Dick, Alexander

Wendland, Holger. A high-order approximation method for semilinear parabolic equations on

spheres, 227Westphal, C. R. See Bidwell, S.

Wu, Shuxia. See Liu, Xiaoji

Wuthrich, Christian. See Stein, WilliamXie, Ziqing, Li-Lian Wang, and Xiaodan Zhao. On exponential convergence of Gegenbauer in-

terpolation and spectral differentiation, 1017

Xing, Y. See Bona, J. L.Xing, Yulong. See Feng, Xiaobing

Xu, Jinchao. See Wang, MingXue, Jungong, and Qiang Ye. Computing exponentials of essentially non-negative matrices en-

trywise to high relative accuracy, 1577

Yadav, Sangita, Amiya K. Pani, and Eun-Jae Park. Superconvergent discontinuous Galerkinmethods for nonlinear elliptic equations, 1297

Yang, Junfeng, and Xiaoming Yuan. Linearized augmented Lagrangian and alternating direction

methods for nuclear norm minimization, 301Yang, Yi, Michael Moller, and Stanley Osher. A dual split Bregman method for fast `1 mini-

mization, 2061

Yao, Xudong. A minimax method for finding saddle critical points of upper semi-differentiablelocally Lipschitz continuous functional in Hilbert space and its convergence, 2087

Ye, Qiang. See Xue, Jungong

Yuan, Xiaoming. See Yang, JunfengZhang, C. See Papageorgiou, A.

Zhang, Yong, and Tianxin Cai. n-tuples of positive integers with the same sum and the sameproduct, 617

Zhang, Yong, Bin Dong, and Zhaosong Lu. `0 Minimization for wavelet frame based image

restoration, 995Zhao, Hongkai. See Gao, Hao

Zhao, Junjian. See Liu, Youming

Zhao, Xiaodan. See Xie, ZiqingZhlobich, Pavel. See Dopico, Froilan M.

Zhou, Kun. See Du, Qiang

Zhuang, Xiaosheng. See Han, BinZimmermann, Paul. See Melquiond, Guillaume

VOLUME 82 2013

A M E R I C A N M A T H E M A T I C A L S O C I E T Y

EDITED BY

Remi AbgrallSusanne C. Brenner, Managing EditorDaniela CalvettiZhiming ChenRonald F. A. CoolsRicardo G. DuranVivette GiraultNicholas I. M. GouldDouglas HardinFred J. HickernellGregor KemperBoris N. KhoromskijStig LarssonChristian LubichGunter MalleMichael J. MossinghoffStanley OsherGilles PagesCheryl E. PraegerRenate ScheidlerChristoph SchwabJie ShenZuowei ShenIgor E. ShparlinskiChi-Wang ShuChris SmythDaniel B. SzyldMark van HoeijHans VolkmerYa-xiang YuanZhimin Zhang

PROVIDENCE, RHODE ISLAND USA

ISSN 0025-5718 (print)ISSN 1088-6842 (online)

Mathematics of Computation

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10 9 8 7 6 5 4 3 2 1 18 17 16 15 14 13

MATHEMATICS OF COMPUTATION

CONTENTS

Vol. 82, No. 281 January 2013

Gerhard Dziuk and Charles M. Elliott, L2-estimates for the evolvingsurface finite element method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Ming Wang and Jinchao Xu, Minimal finite element spaces for 2m-th-order partial differential equations in Rn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Georgios Akrivis, Implicit–explicit multistep methods for nonlinearparabolic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Wei Gong, Error estimates for finite element approximations of parabolicequations with measure data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Weizhu Bao and Yongyong Cai, Optimal error estimates of finitedifference methods for the Gross-Pitaevskii equation with angularmomentum rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Nikolaos Sfakianakis, Adaptive mesh reconstruction for hyperbolicconservation laws with total variation bound . . . . . . . . . . . . . . . . . . . . . . . . . 129

Hao Gao and Hongkai Zhao, Analysis of a numerical solver for radiativetransport equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

Helge Holden, Christian Lubich, and Nils Henrik Risebro, Operatorsplitting for partial differential equations with Burgers nonlinearity . . . 173

Bernardo Cockburn, Ivan Merev, and Jianliang Qian, Locala posteriori error estimates for time-dependent Hamilton-Jacobiequations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

Houde Han and Zhongyi Huang, Tailored finite point method based onexponential bases for convection-diffusion-reaction equation . . . . . . . . . . 213

Holger Wendland, A high-order approximation method for semilinearparabolic equations on spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

Ralf Hiptmair, Andrea Moiola, and Ilaria Perugia, Error analysis ofTrefftz-discontinuous Galerkin methods for the time-harmonic Maxwellequations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

Martin Burger, Michael Moller, Martin Benning, and StanleyOsher, An adaptive inverse scale space method for compressed sensing 269

Junfeng Yang and Xiaoming Yuan, Linearized augmented Lagrangianand alternating direction methods for nuclear norm minimization . . . . . 301

Y. Lipman, J. Puente, and I. Daubechies, Conformal Wassersteindistance: II. computational aspects and extensions . . . . . . . . . . . . . . . . . . . . 331

Michael Griebel, Frances Y. Kuo, and Ian H. Sloan, The smoothingeffect of integration in Rd and the ANOVA decomposition . . . . . . . . . . . . 383

Youming Liu and Junjian Zhao, An extension of Bittner and Urban’stheorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401

Guo Ben-yu, Sun Tao, and Zhang Chao, Jacobi and Laguerre quasi-orthogonal approximations and related interpolations . . . . . . . . . . . . . . . . . 413

Bela Bollobas, Malte Lackmann, and Dierk Schleicher, A smallprobabilistic universal set of starting points for finding roots of complexpolynomials by Newton’s method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

Bin Han and Xiaosheng Zhuang, Algorithms for matrix extension andorthogonal wavelet filter banks over algebraic number fields . . . . . . . . . . 459

Reza R. Farashahi, Pierre-Alain Fouque, Igor E. Shparlinski,Mehdi Tibouchi, and J. Felipe Voloch, Indifferentiable determinis-tic hashing to elliptic and hyperelliptic curves . . . . . . . . . . . . . . . . . . . . . . . . 491

Robert L. Miller and Michael Stoll, Explicit isogeny descent on ellipticcurves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

Takafumi Shibuta, Irreducibility criterion for algebroid curves . . . . . . . . . . . 531

Koray Karabina, Squaring in cyclotomic subgroups . . . . . . . . . . . . . . . . . . . . . . 555

Sorina Ionica and Antoine Joux, Pairing the volcano . . . . . . . . . . . . . . . . . . 581

Anderson N. Martinhao and Emerson L. Monte Carmelo, Shortcovering codes arising from matchings in weighted graphs . . . . . . . . . . . . 605

Yong Zhang and Tianxin Cai, n-tuples of positive integers with the samesum and the same product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617

Vol. 82, No. 282 April 2013

Alan Demlow and Stig Larsson, Local pointwise a posteriori gradienterror bounds for the Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625

Bernardo Cockburn and Ke Shi, Conditions for superconvergence of HDGmethods for Stokes flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651

S. Bidwell, M. E. Hassell, and C. R. Westphal, A weighted least squaresfinite element method for elliptic problems with degenerate and singularcoefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673

D. C. Antonopoulos and V. A. Dougalis, Error estimates for Galerkinapproximations of the “classical” Boussinesq system . . . . . . . . . . . . . . . . . . 689

Helge Holden, Kenneth H. Karlsen, and Trygve Karper, Operatorsplitting for two-dimensional incompressible fluid equations . . . . . . . . . . . 719

Shi Jin, Jian-guo Liu, and Li Wang, A domain decomposition method forsemilinear hyperbolic systems with two-scale relaxations . . . . . . . . . . . . . . 749

Bengt Hakberg, A discrete KPP-theory for Fisher’s equation . . . . . . . . . . . . 781

Samuel K. M. Chenoweth, Julio Soria, and Andrew Ooi, An improvedinterpolation scheme for finite volume simulations on unstructuredmeshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803

Christophe Berthon, Philippe G. LeFloch, and Rodolphe Turpault,Late-time/stiff-relaxation asymptotic-preserving approximations of hy-perbolic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831

Vladimir Molchanov and Marcel Oliver, Convergence of the Hamilton-ian particle-mesh method for barotropic fluid flow . . . . . . . . . . . . . . . . . . . . 861

Alexander Dick, Othmar Koch, Roswitha Marz, and EwaWeinmuller, Convergence of collocation schemes for boundary valueproblems in nonlinear index 1 DAEs with a singular point . . . . . . . . . . . . 893

Hailiang Liu, Olof Runborg, and Nicolay M. Tanushev, Errorestimates for Gaussian beam superpositions . . . . . . . . . . . . . . . . . . . . . . . . . . 919

V. L. Makarov, D. V. Dragunov, and Ya. V. Klimenko, The FD-method for solving Sturm-Liouville problems with special singulardifferential operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953

Michael Griebel and Helmut Harbrecht, On the construction of sparsetensor product spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 975

Yong Zhang, Bin Dong, and Zhaosong Lu, `0 Minimization for waveletframe based image restoration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995

Ziqing Xie, Li-Lian Wang, and Xiaodan Zhao, On exponentialconvergence of Gegenbauer interpolation and spectral differentiation . . 1017

Miodrag M. Spalevic, Error bounds of Gaussian quadrature formulae forone class of Bernstein-Szego weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1037

Kenier Castillo and Francisco Marcellan, Generators of rational spectraltransformations for nontrivial C-functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1057

Ivan Area, Dimitar K. Dimitrov, Eduardo Godoy, and VanessaG. Paschoa, Zeros of classical orthogonal polynomials of a discretevariable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1069

Stamatis Koumandos and Martin Lamprecht, Complete monotonicityand related properties of some special functions . . . . . . . . . . . . . . . . . . . . . . 1097

Timothy Caley, The Prouhet-Tarry-Escott problem for Gaussian integers 1121

Daniel J. Bernstein, Peter Birkner, Tanja Lange, and ChristianePeters, ECM using Edwards curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1139

Steven D. Galbraith, John M. Pollard, and Raminder S. Ruprai,Computing discrete logarithms in an interval . . . . . . . . . . . . . . . . . . . . . . . . . 1181

Kevin G. Hare and Maysum Panju, Some comments on Garsia numbers 1197

Xavier Guitart and Marc Masdeu, Continued fractions in 2-stageEuclidean quadratic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1223

Guillaume Melquiond, W. Georg Nowak, and Paul Zimmermann,Numerical approximation of The Masser-Gramain constant to fourdecimal digits: δ = 1.819... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1235

Vol. 82, No. 283 July 2013

Adrian Hirn, Finite element approximation of singular power-law systems 1247

Xiaobing Feng and Yulong Xing, Absolutely stable local discontinuousGalerkin methods for the Helmholtz equation with large wave number 1269

Sangita Yadav, Amiya K. Pani, and Eun-Jae Park, Superconvergentdiscontinuous Galerkin methods for nonlinear elliptic equations . . . . . . . 1297

Chuanmiao Chen and Shufang Hu, The highest order superconvergencefor bi-k degree rectangular elements at nodes: A proof of 2k-conjecture 1337

Traian Iliescu and Zhu Wang, Variational multiscale proper orthogo-nal decomposition: Convection-dominated convection-diffusion-reactionequations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1357

Paola F. Antonietti, Lourenco Beirao da Veiga, and Marco Verani,A mimetic discretization of elliptic obstacle problems . . . . . . . . . . . . . . . . . 1379

J. L. Bona, H. Chen, O. Karakashian, and Y. Xing, Conservative,discontinuous Galerkin–methods for the generalized Korteweg–de Vriesequation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1401

Kristian Debrabant and Espen R. Jakobsen, Semi-Lagrangian schemesfor linear and fully non-linear diffusion equations . . . . . . . . . . . . . . . . . . . . . 1433

N. V. Krylov, Interior estimates for second-order differences of solutions offinite-difference elliptic Bellman’s equations . . . . . . . . . . . . . . . . . . . . . . . . . . 1463

Simone Cifani and Espen R. Jakobsen, On the spectral vanishingviscosity method for periodic fractional conservation laws . . . . . . . . . . . . . 1489

Claude Jeffrey Gittelson, An adaptive stochastic Galerkin method forrandom elliptic operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1515

Yoshitaka Watanabe, Takehiko Kinoshita, and Mitsuhiro T. Nakao,A posteriori estimates of inverse operators for boundary value problemsin linear elliptic partial differential equations . . . . . . . . . . . . . . . . . . . . . . . . . 1543

S. Blanes, F. Casas, P. Chartier, and A. Murua, Optimized high-ordersplitting methods for some classes of parabolic equations . . . . . . . . . . . . . 1559

Jungong Xue and Qiang Ye, Computing exponentials of essentially non-negative matrices entrywise to high relative accuracy . . . . . . . . . . . . . . . . . 1577

Xiaoji Liu, Shuxia Wu, and Dragana S. Cvetkovic-Ilic, Newresults on reverse order law for {1, 2, 3}- and {1, 2, 4}-inverses of boundedoperators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1597

Shuai Lu and Peter Mathe, Heuristic parameter selection based onfunctional minimization: Optimality and model function approach . . . . 1609

Shidong Jiang, Zhi Liang, and Jingfang Huang, A fast algorithm forBrownian dynamics simulation with hydrodynamic interactions . . . . . . . 1631

Qinian Jin, Further convergence results on the general iteratively regularizedGauss-Newton methods under the discrepancy principle . . . . . . . . . . . . . . 1647

Elaine Cohen, Tom Lyche, and Richard F. Riesenfeld, A B-spline-likebasis for the Powell-Sabin 12-split based on simplex splines . . . . . . . . . . . 1667

Rados law Szmytkowski, Erratum to “Formulas and Theorems forthe Special Functions of Mathematical Physics” by W. Magnus,F. Oberhettinger, R. P. Soni . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1709

Peter Bruin, Computing in Picard groups of projective curves over finitefields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1711

William Stein and Christian Wuthrich, Algorithms for the arithmetic ofelliptic curves using Iwasawa theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1757

Guillaume Cheze, A recombination algorithm for the decomposition ofmultivariate rational functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1793

M. Delgado, J. I. Farran, P. A. Garcıa-Sanchez, and D. Llena, Onthe generalized Feng-Rao numbers of numerical semigroups generated byintervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1813

Johan Sejr Brinch Nielsen and Jakob Grue Simonsen, Anexperimental investigation of the normality of irrational algebraicnumbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1837

Vol. 82, No. 284 October 2013

Alexey Chernov and Christoph Schwab, First order k-th moment finiteelement analysis of nonlinear operator equations with stochastic data . 1859

Qiang Du, Lili Ju, Li Tian, and Kun Zhou, A posteriori error analysisof finite element method for linear nonlocal diffusion and peridynamicmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1889

Tan Bui-Thanh, Leszek Demkowicz, and Omar Ghattas, Construc-tively well-posed approximation methods with unity inf–sup and conti-nuity constants for partial differential equations . . . . . . . . . . . . . . . . . . . . . . 1923

Ross Ingram, A new linearly extrapolated Crank-Nicolson time-steppingscheme for the Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1953

Eskil Hansen and Tony Stillfjord, Convergence of the implicit-explicitEuler scheme applied to perturbed dissipative evolution equations . . . . 1975

Kassem Mustapha, A Superconvergent discontinuous Galerkin method forVolterra integro-differential equations, smooth and non-smooth kernels 1987

Froilan M. Dopico, Vadim Olshevsky, and Pavel Zhlobich, Stability ofQR-based fast system solvers for a subclass of quasiseparable rank onematrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2007

Carl Jagels and Lothar Reichel, The structure of matrices in rationalGauss quadrature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2035

Yi Yang, Michael Moller, and Stanley Osher, A dual split Bregmanmethod for fast `1 minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2061

Xudong Yao, A minimax method for finding saddle critical points of uppersemi-differentiable locally Lipschitz continuous functional in Hilbertspace and its convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2087

Christine Choirat and Raffaello Seri, Computational aspects of Cui-Freeden statistics for equidistribution on the sphere . . . . . . . . . . . . . . . . . . 2137

Nabi Chegini, Stephan Dahlke, Ulrich Friedrich, and RobStevenson, Piecewise tensor product wavelet bases by extensions andapproximation rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2157

C. Ortner and A. V. Shapeev, Analysis of an energy-basedatomistic/continuum approximation of a vacancy in the 2D triangularlattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2191

Ana Romero and Julio Rubio, Homotopy groups of suspended classifyingspaces: An experimental approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2237

Claude-Pierre Jeannerod, Nicolas Louvet, and Jean-Michel Muller,Further analysis of Kahan’s algorithm for the accurate computation of2× 2 determinants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2245

Mark W. Coffey and George Csordas, On the log-concavity of a Jacobitheta function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2265

Georges Klein, An extension of the Floater–Hormann family of barycentricrational interpolants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2273

A. Papageorgiou, I. Petras, J. F. Traub, and C. Zhang, Afast algorithm for approximating the ground state energy on a quantumcomputer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2293

Michael Strauss, The second order spectrum and optimal convergence . . . 2305

A. Bayad and J. Chikhi, Mobius inversion formulae for Apostol-Bernoullitype polynomials and numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2327

Tianxin Cai and Deyi Chen, A new variant of the Hilbert-Waring problem 2333

Anna Morra, An algorithm to compute relative cubic fields . . . . . . . . . . . . . . 2343

Werner Bley and Ruben Debeerst, Algorithmic proof of the epsilonconstant conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2363

Robert Granger and Andrew Moss, Generalised Mersenne numbersrevisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2389

Murray R. Bremner and Jiaxiong Hu, Fundamental invariants for theaction of SL3(C)× SL3(C)× SL3(C) on 3× 3× 3 arrays . . . . . . . . . . . . 2421

Kevin Broughan, Sergio Guzman Sanchez, and Florian Luca, Perfectrepdigits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2439

Editorial Information

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Editorial Committee

SUSANNE C. BRENNER, Chair, Center for Computation and Technology, JohnstonHall, Louisiana State University, Baton Rouge, LA 70803 USA; E-mail : mathcomp@

math.lsu.edu

RONALD F. A. COOLS, Department of Computer Science, Katholieke UniversiteitLeuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium; E-mail : ronald.cools@cs.

kuleuven.ac.be

IGOR E. SHPARLINSKI, Department of Computing, Macquarie University, Sydney,New South Wales 2109, Australia; E-mail : igor.shparlinski@mq.edu.au

CHI-WANG SHU, Applied Mathematics Division, Brown University, P.O. Box F, 182George St., Providence, RI 02912-0001 USA; E-mail : mathcomp@dam.brown.edu

Board of Associate Editors

REMI ABGRALL, INRIA & Institut Polytechnique de Bordeaux, Team Bacchus andInstitut de Mathematiques de Bordeaux, Bat A29 bis, 351 cours de la Liberation, 33 405Talence, Cedex France; E-mail : abgrall@math.u-bordeaux.fr

DANIELA CALVETTI, Department of Mathematics, CaseWestern Reserve University,Yost Hall, 10900 Euclid Avenue., Cleveland, OH 44106 USA; E-mail : daniela.calvetti@case.edu

ZHIMING CHEN, Institute of Computational Mathematics, Chinese Academy of Sci-ences, P.O. Box 2719, Beijing 100080, China; E-mail : zmchen@lsec.cc.ac.cn

RICARDO G. DURAN, Department of Mathematics, University of Buenos Aires, Ciu-dad Universitaria, Pabellon I, 1428 Buenos Aires, Argentina; E-mail : rduran@dm.uba.ar

VIVETTE GIRAULT, Laboratoire Jacques-Louis Lions, Boite courrier 187, Univer-site de Pierre et Marie Curie, 4, place Jussieu, 75252 Paris Cedex 05, France; E-mail :girault@ann.jussieu.fr

NICHOLAS I. M. GOULD, Department of Scientific Computing, G59, R18 STFC-Rutherford Appleton Laboratory, Chilton, Oxon OX11 0QX England; E-mail : nick.gould@stfc.ac.uk

DOUGLAS HARDIN, Vanderbilt University Department of Mathematics 1326 Steven-son Center Nashville, TN 37240 USA; E-mail : doug.hardin@vanderbilt.edu

FRED J. HICKERNELL, Department of Applied Mathematics, Illinois Institute ofTechnology, E1 Building, Room 208, 10 W. 32nd Street, Chicago, IL 60616-3793 USA;E-mail : hickernell@iit.edu

GREGOR KEMPER, Technische Universitat Munchen, Zentrum Mathematik M 11,Boltzmannstr 3, 85748 Garching, Germany; E-mail : kemper@ma.tum.de

BORIS N. KHOROMSKIJ, Max Planck Institute for Mathematics in the Sciences,Inselstr. 22-26, D-04103 Leipzig, Germany; E-mail : bokh@mis.mpg.de

STIG LARSSON, Department of Mathematical Sciences, Chalmers University of Tech-nology, SE-412 96 Gothenburg, Sweden; E-mail : stig@chalmers.se

CHRISTIAN LUBICH, Universitat Tubingen, Mathematik, Auf der Morgenstelle 10,72076 Tubengen; E-mail : lubich@na.uni-tuebingen.de

GUNTERMALLE, Fachbereich Mathematik, Universitat Kaiserslautern, Postfach 3049,67653 Kaiserslautern, Germany; E-mail : malle@mathematik.uni-kl.de

MICHAEL J. MOSSINGHOFF, Department of Mathematics, Davidson College, David-son, NC 28035-6996 USA; E-mail : mimossinghoff@davidson.edu

STANLEY OSHER, Department of Mathematics, University of California, P.O. Box951555, Los Angeles, CA 90095-1555 USA; E-mail : sjo@math.ucla.edu

GILLES PAGES, University of Paris VI, Case courrier 188, 4, place Jussieu, 75252Paris, Cedex 05, France; E-mail : gilles.pages@upmc.fr

CHERYL E. PRAEGER, School of Mathematics and Statistics, M019, University ofWestern Australia, 35 Stirling Highway, Crawley 6009, Western Australia, Australia;E-mail : praeger@maths.uwa.edu.au

RENATE SCHEIDLER, Department of Mathematics and Statistics, MS 364, Univer-sity of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada; E-mail :rscheidl@math.ucalgary.ca

CHRISTOPH SCHWAB, Seminar of Applied Mathematics, ETHZ, 8092 Zurich,Switzerland; E-mail : christoph.schwab@sam.math.ethz.ch

JIE SHEN, Department of Mathematics, Purdue University, West Lafayette, IN 47907USA; E-mail : shen@math.purdue.edu

ZUOWEI SHEN, Department of Mathematics, National University of Singapore, BlockS17 10, Lower Kent Ridge Road, 119076 Singapore; E-mail : matzuows@nus.edu.sg

CHRIS SMYTH, School of Mathematics, The University of Edinburgh, James ClerkMaxwell Building, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, United King-dom; E-mail : C.Smyth@ed.ac.uk

DANIEL B. SZYLD, Department of Mathematics, Temple University (038-16), 1805N. Broad Street, Philadelphia, PA 19122-6094 USA; E-mail : szyld@temple.edu

MARK van HOEIJ, Department of Mathematics, Florida State University, 1017 Aca-demic Way, Tallahassee, FL 32306 USA; E-mail : hoeij@math.fsu.edu

HANS VOLKMER, Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201-0413 USA; E-mail : volkmer@csd.uwm.edu

YA-XIANG YAUN, Chinese Academy of Science, LSEC AMSS, Beijing, 100190 PeoplesRepublic of China; E-mail : yyx@lsec.cc.ac.cn

ZHIMIN ZHANG, Department of Mathematics, Wayne State University, Detroit, MI48202 USA; E-mail : zzhang@math.wayne.edu

(Continued from back cover)

Georges Klein, An extension of the Floater–Hormann family of barycentricrational interpolants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2273

A. Papageorgiou, I. Petras, J. F. Traub, and C. Zhang, A fastalgorithm for approximating the ground state energy on a quantumcomputer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2293

Michael Strauss, The second order spectrum and optimal convergence . . . 2305

A. Bayad and J. Chikhi, Mobius inversion formulae for Apostol-Bernoullitype polynomials and numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2327

Tianxin Cai and Deyi Chen, A new variant of the Hilbert-Waringproblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2333

Anna Morra, An algorithm to compute relative cubic fields . . . . . . . . . . . . . . 2343

Werner Bley and Ruben Debeerst, Algorithmic proof of the epsilonconstant conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2363

Robert Granger and Andrew Moss, Generalised Mersenne numbersrevisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2389

Murray R. Bremner and Jiaxiong Hu, Fundamental invariants for theaction of SL3(C) × SL3(C) × SL3(C) on 3 × 3 × 3 arrays . . . . . . . . . . . . 2421

Kevin Broughan, Sergio Guzman Sanchez, and Florian Luca, Perfectrepdigits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2439

MATHEMATICS OF COMPUTATION

CONTENTS

Vol. 82, No. 284 October 2013

Alexey Chernov and Christoph Schwab, First order k-th moment finiteelement analysis of nonlinear operator equations with stochastic data 1859

Qiang Du, Lili Ju, Li Tian, and Kun Zhou, A posteriori error analysisof finite element method for linear nonlocal diffusion and peridynamicmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1889

Tan Bui-Thanh, Leszek Demkowicz, and Omar Ghattas, Construc-tively well-posed approximation methods with unity inf–sup and conti-nuity constants for partial differential equations . . . . . . . . . . . . . . . . . . . . . . 1923

Ross Ingram, A new linearly extrapolated Crank-Nicolson time-steppingscheme for the Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1953

Eskil Hansen and Tony Stillfjord, Convergence of the implicit-explicitEuler scheme applied to perturbed dissipative evolution equations . . . . 1975

Kassem Mustapha, A Superconvergent discontinuous Galerkin method forVolterra integro-differential equations, smooth and non-smooth kernels 1987

Froilan M. Dopico, Vadim Olshevsky, and Pavel Zhlobich, Stabilityof QR-based fast system solvers for a subclass of quasiseparable rankone matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2007

Carl Jagels and Lothar Reichel, The structure of matrices in rationalGauss quadrature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2035

Yi Yang, Michael Moller, and Stanley Osher, A dual split Bregmanmethod for fast `1 minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2061

Xudong Yao, A minimax method for finding saddle critical points of uppersemi-differentiable locally Lipschitz continuous functional in Hilbertspace and its convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2087

Christine Choirat and Raffaello Seri, Computational aspects of Cui-Freeden statistics for equidistribution on the sphere . . . . . . . . . . . . . . . . . . 2137

Nabi Chegini, Stephan Dahlke, Ulrich Friedrich, and RobStevenson, Piecewise tensor product wavelet bases by extensions andapproximation rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2157

C. Ortner and A. V. Shapeev, Analysis of an energy-basedatomistic/continuum approximation of a vacancy in the 2D triangularlattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2191

Ana Romero and Julio Rubio, Homotopy groups of suspended classifyingspaces: An experimental approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2237

Claude-Pierre Jeannerod, Nicolas Louvet, and Jean-Michel Muller,Further analysis of Kahan’s algorithm for the accurate computation of2 × 2 determinants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2245

Mark W. Coffey and George Csordas, On the log-concavity of a Jacobitheta function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2265

(Continued on inside back cover)

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