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VOLUME 87 NUMBER 314 NOVEMBER 2018

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. 87, No. 314 November 2018

Lenaıc Chizat, Gabriel Peyre, Bernhard Schmitzer, and Francois-Xavier Vialard, Scaling algorithms for unbalanced optimal transportproblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2563

Christian Kreuzer and Emmanuil H. Georgoulis, Convergence ofadaptive discontinuous Galerkin methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2611

Paul Houston and Thomas P. Wihler, An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear ellipticboundary value problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2641

Andrea Cangiani, Emmanuil H. Georgoulis, and Younis A. Sabawi,Adaptive discontinuous Galerkin methods for elliptic interface problems 2675

Jeonghun J. Lee and Ragnar Winther, Local coderivatives andapproximation of Hodge Laplace problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 2709

Siyang Wang, Anna Nissen, and Gunilla Kreiss, Convergence of finitedifference methods for the wave equation in two space dimensions . . . . 2737

Ralf Kornhuber, Daniel Peterseim, and Harry Yserentant, Ananalysis of a class of variational multiscale methods based on subspacedecomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2765

Eliane Becache, Patrick Joly, and Valentin Vinoles, On the analysis ofperfectly matched layers for a class of dispersive media and applicationto negative index metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2775

Dario A. Bini, Stefano Massei, and Beatrice Meini, Semi-infinite quasi-Toeplitz matrices with applications to QBD stochastic processes . . . . . 2811

Yang Zhou and Xiaojun Chen, Spherical tε-designs for approximationson the sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2831

Zhijian He, Quasi-Monte Carlo for discontinuous integrands withsingularities along the boundary of the unit cube . . . . . . . . . . . . . . . . . . . . 2857

Jared Duker Lichtman and Carl Pomerance, Improved error boundsfor the Fermat primality test on random inputs . . . . . . . . . . . . . . . . . . . . . . 2871

Andrew R. Booker, Finite connected components of the aliquot graph . . 2891

Stal Aanderaa, Lars Kristiansen, and Hans Kristian Ruud, Searchfor good examples of Hall’s conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2903

Markus Hittmeir, A babystep-giantstep method for faster deterministicinteger factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2915

Jonathan W. Sands and Brett A. Tangedal, Computing annihilators ofclass groups from derivatives of L-functions . . . . . . . . . . . . . . . . . . . . . . . . . . 2937

Philip Brinkmann and Gunter M. Ziegler, Small f -vectors of 3-spheresand of 4-polytopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2955

Frederic Chyzak, Thomas Dreyfus, Philippe Dumas, and MarcMezzarobba, Computing solutions of linear Mahler equations . . . . . . 2977

Javier Cilleruelo, Florian Luca, and Lewis Baxter, Every positiveinteger is a sum of three palindromes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3023

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INDEX TO VOLUME 87 (2018)

Aanderaa, Stal, Lars Kristiansen, and Hans Kristian Ruud. Search for good examples of Hall’s

conjecture, 2903

Acosta, Gabriel, Juan Pablo Borthagaray, Oscar Bruno, and Martın Maas. Regularity theoryand high order numerical methods for the (1D)-fractional Laplacian, 1821

Altmann, R., and C. Zimmer. Runge-Kutta methods for linear semi-explicit operator differential-

algebraic equations, 149Angot, Philippe, and Rima Cheaytou. On the error estimates of the vector penalty-projection

methods: Second-order scheme, 2159Banjai, Lehel, and Alexander Rieder. Convolution quadrature for the wave equation with a non-

linear impedance boundary condition, 1783

Bao, Weizhu, and Chunmei Su. Uniform error bounds of a finite difference method for the Klein-Gordon-Zakharov system in the subsonic limit regime, 2133

Baumstark, Simon, Erwan Faou, and Katharina Schratz. Uniformly accurate exponential-type

integrators for Klein-Gordon equations with asymptotic convergence to the classical NLSsplitting, 1227

Baxter, Lewis. See Cilleruelo, Javier

Becache, Eliane, Patrick Joly, and Valentin Vinoles. On the analysis of perfectly matched layers

for a class of dispersive media and application to negative index metamaterials, 2775

Bini, Dario A., Stefano Massei, and Beatrice Meini. Semi-infinite quasi-Toeplitz matrices withapplications to QBD stochastic processes, 2811

Birgin, E. G., N. Krejic, and J. M. Martınez. On the employment of inexact restoration for the

minimization of functions whose evaluation is subject to errors, 1307Booker, Andrew R. Finite connected components of the aliquot graph, 2891

Borm, Steffen. Adaptive compression of large vectors, 209

Borthagaray, Juan Pablo. See Acosta, GabrielBras-Amoros, Maria, and Julio Fernandez-Gonzalez. Computation of numerical semigroups by

means of seeds, 2539

Bringmann, Bjoern, Daniel Cremers, Felix Krahmer, and Michael Moeller. The homotopy methodrevisited: Computing solution paths of `1-regularized problems, 2343

Brinkmann, Philip, and Gunter M. Ziegler. Small f-vectors of 3-spheres and of 4-polytopes, 2955Broersen, D., W. Dahmen, and R. P. Stevenson. On the stability of DPG formulations of trans-

port equations, 1051

Brugiapaglia, Simone, Fabio Nobile, Stefano Micheletti, and Simona Perotto. A theoretical studyof COmpRessed SolvING for advection-diffusion-reaction problems, 1

Bruin, Peter, and Andrea Ferraguti. On L-functions of quadratic Q-curves, 459

Bruno, Oscar. See Acosta, GabrielBurgos Gil, Jose Ignacio, Ricardo Menares, and Juan Rivera-Letelier. On the essential minimum

of Faltings’ height, 2425

Burman, Erik, and Peter Hansbo. Stabilized nonconforming finite element methods for dataassimilation in incompressible flows, 1029

Burman, Erik, Peter Hansbo, and Mats G. Larson. A cut finite element method with boundary

value correction, 633Buthe, Jan. An analytic method for bounding ψ(x), 1991

Cai, Yongyong, and Jie Shen. Error estimates for a fully discretized scheme to a Cahn-Hilliardphase-field model for two-phase incompressible flows, 2057

Cai, Yongyong, and Yongjun Yuan. Uniform error estimates of the conservative finite differencemethod for the Zakharov system in the subsonic limit regime, 1191

Cangiani, Andrea, Emmanuil H. Georgoulis, and Younis A. Sabawi. Adaptive discontinuousGalerkin methods for elliptic interface problems, 2675

Charles, Zachary. Generating random factored ideals in number fields, 2047Cheaytou, Rima. See Angot, PhilippeChen, Long, Jun Hu, and Xuehai Huang. Fast auxiliary space preconditioners for linear elasticity

in mixed form, 1601Chen, Xiaojun. See Zhou, Yang

Chen, Zhangxin. See He, Ruijian

Cheng, Wanyou, and Yu-Hong Dai. Gradient-based method with active set strategy for `1 opti-mization, 1283

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Chizat, Lenaıc, Gabriel Peyre, Bernhard Schmitzer, and Francois-Xavier Vialard. Scaling algo-

rithms for unbalanced optimal transport problems, 2563

Chkifa, Abdellah, Nick Dexter, Hoang Tran, and Clayton G. Webster. Polynomial approximationvia compressed sensing of high-dimensional functions on lower sets, 1415

Christiansen, Snorre H. On eigenmode approximation for Dirac equations: Differential forms

and fractional Sobolev spaces, 547Chyzak, Frederic, Thomas Dreyfus, Philippe Dumas, and Marc Mezzarobba. Computing solu-

tions of linear Mahler equations, 2977

Cilleruelo, Javier, Florian Luca, and Lewis Baxter. Every positive integer is a sum of threepalindromes, 3023

Coquel, Frederic, Shi Jin, Jian-Guo Liu, and Li Wang. Entropic sub-cell shock capturing schemes

via Jin-Xin relaxation and Glimm front sampling for scalar conservation laws, 1083Cravero, I., G. Puppo, M. Semplice, and G. Visconti. CWENO: Uniformly accurate reconstruc-

tions for balance laws, 1689Cremers, Daniel. See Bringmann, Bjoern

D ↪abrowski, Andrzej, and Lucjan Szymaszkiewicz. Orders of Tate-Shafarevich groups for the

Neumann-Setzer type elliptic curves, 1509Dahmen, W. See Broersen, D.

Dai, Yu-Hong. See Cheng, Wanyou

Daniels, Harris B., Alvaro Lozano-Robledo, Filip Najman, and Andrew V. Sutherland. Torsion

subgroups of rational elliptic curves over the compositum of all cubic fields, 425

Detinko, A., D. L. Flannery, and A. Hulpke. Zariski density and computing in arithmetic groups,967

Dexter, Nick. See Chkifa, Abdellah

DiPasquale, Michael. Dimension of mixed splines on polytopal cells, 905Dohrmann, Clark R. See Oh, Duk-Soon

Dreyfus, Thomas. See Chyzak, Frederic

Drungilas, P., J. Jankauskas, and J. Siurys. On Littlewood and Newman polynomial multiples ofBorwein polynomials, 1523

Dumas, Philippe. See Chyzak, Frederic

Efremenko, Klim, J. M. Landsberg, Hal Schenck, and Jerzy Weyman. The method of shiftedpartial derivatives cannot separate the permanent from the determinant, 2037

Elsey, Matt, and Selim Esedoglu. Threshold dynamics for anisotropic surface energies, 1721

Ervin, V. J., N. Heuer, and J. P. Roop. Regularity of the solution to 1-D fractional order diffusionequations, 2273

Esedoglu, Selim. See Elsey, MattFaber, Laura, and Habiba Kadiri. Corrigendum to New bounds for ψ(x), 1451

Faou, Erwan. See Baumstark, Simon

Feng, Ruyong. On the computation of the Galois group of linear difference equations, 941Feng, Xinlong. See He, Ruijian

Fernandez-Gonzalez, Julio. See Bras-Amoros, MariaFerraguti, Andrea. See Bruin, PeterFlannery, D. L. See Detinko, A.

Franz, Sebastian, and Gunar Matthies. A unified framework for time-dependent singularly per-turbed problems with discontinuous Galerkin methods in time, 2113

Freitas, Pedro. Sharp bounds for the modulus and phase of Hankel functions with applications

to Jaeger integrals, 289

Friedland, Shmuel, and Lek-Heng Lim. Nuclear norm of higher-order tensors, 1255Fung, King Cheong, and Ben Kane. On sign changes of cusp forms and the halting of an algo-

rithm to construct a supersingular elliptic curve with a given endomorphism ring, 501Gallouet, T., R. Herbin, J.-C. Latche, and D. Maltese. Convergence of the MAC scheme for the

compressible stationary Navier-Stokes equations, 1127

Gander, Martin J., and Soheil Hajian. Analysis of Schwarz methods for a hybridizable discon-tinuous Galerkin discretization: The many-subdomain case, 1635

Georgoulis, Emmanuil H. See Cangiani, Andrea. See Kreuzer, Christian

Glaubitz, Jan, Philipp Offner, and Thomas Sonar. Application of modal filtering to a spectral

difference method, 175












































Gonzalez-Jimenez, Enrique, and Alvaro Lozano-Robledo. On the torsion of rational elliptic

curves over quartic fields, 1457

Grenie, Loıc, and Giuseppe Molteni. Explicit bounds for generators of the class group, 2483Gulliver, T. Aaron. See Rebenich, Niko

Guzman, Johnny, and Maxim Olshanskii. Inf-sup stability of geometrically unfitted Stokes finite

elements, 2091Hadjimichael, Yiannis, and David I. Ketcheson. Strong-stability-preserving additive linear mul-

tistep methods, 2295

Hajian, Soheil. See Gander, Martin J.Han, Bin, Qingtang Jiang, Zuowei Shen, and Xiaosheng Zhuang. Symmetric canonical quincunx

tight framelets with high vanishing moments and smoothness, 347

Hangelbroek, T., F. J. Narcowich, C. Rieger, and J. D. Ward. An inverse theorem for compactLipschitz regions in Rd using localized kernel bases, 1949

Hansbo, Peter. See Burman, ErikHe, Ruijian, Xinlong Feng, and Zhangxin Chen. H1-Superconvergence of a difference finite ele-

ment method based on the P1 −P1-conforming element on non-uniform meshes for the 3D

Poisson equation, 1659He, Zhijian. Quasi-Monte Carlo for discontinuous integrands with singularities along the bound-

ary of the unit cube, 2857

Herbin, R. See Gallouet, T.Heuer, N. See Ervin, V. J.

Hittmeir, Markus. A babystep-giantstep method for faster deterministic integer factorization,

2915Hofmann, Bernd. See Plato, Robert

Houston, Paul, and Thomas P. Wihler. An hp-adaptive Newton-discontinuous-Galerkin finite

element approach for semilinear elliptic boundary value problems, 2641Hu, Jun. See Chen, Long

Huang, Weizhang, and Lennard Kamenski. On the mesh nonsingularity of the moving meshPDE method, 1887

Huang, Xuehai. See Chen, Long

Hulpke, A. See Detinko, A.Hurst, Greg. Computations of the Mertens function and improved bounds on the Mertens con-

jecture, 1013

Hutzenthaler, Martin, Arnulf Jentzen, and Xiaojie Wang. Exponential integrability properties ofnumerical approximation processes for nonlinear stochastic differential equations, 1353

Jankauskas, J. See Drungilas, P.

Jeannerod, Claude-Pierre, and Siegfried M. Rump. On relative errors of floating-point opera-tions: Optimal bounds and applications, 803

Jentzen, Arnulf. See Hutzenthaler, MartinJiang, Qingtang. See Han, BinJiang, Shidong. See Zhang, QianJin, Shi. See Coquel, Frederic

Joly, Patrick. See Becache, Eliane

Ju, Lili, Xiao Li, Zhonghua Qiao, and Hui Zhang. Energy stability and error estimates of ex-ponential time differencing schemes for the epitaxial growth model without slope selection,1859

Kadiri, Habiba. See Faber, Laura

Kamenski, Lennard. See Huang, WeizhangKane, Ben. See Fung, King Cheong

Kemper, Gregor, Ngo Viet Trung, and Nguyen Thi Van Anh. Toward a theory of monomialpreorders, 2513

Ketcheson, David I. See Hadjimichael, Yiannis

King, Oliver D., Cris Poor, Jerry Shurman, and David S. Yuen. Using Katsurada’s determinationof the Eisenstein series to compute Siegel eigenforms, 879

Kokkala, Janne I., and Patric R. J. Ostergard. The chromatic number of the square of the 8-cube,

2551Kornhuber, Ralf, Daniel Peterseim, and Harry Yserentant. An analysis of a class of variational

multiscale methods based on subspace decomposition, 2765






































Krahmer, Felix. See Bringmann, Bjoern

Kreiss, Gunilla. See Wang, Siyang

Krejic, N. See Birgin, E. G.Krenn, Daniel, and Volker Ziegler. Non-minimality of the width-w non-adjacent form in con-

junction with trace one τ -adic digit expansions and Koblitz curves in characteristic two,

821Kreuzer, Christian, and Emmanuil H. Georgoulis. Convergence of adaptive discontinuous Galerkin

methods, 2611

Kristiansen, Lars. See Aanderaa, StalKublik, Catherine, and Richard Tsai. An extrapolative approach to integration over hypersur-

faces in the level set framework, 2365

Kuszmaul, William. Fast algorithms for finding pattern avoiders and counting pattern occur-rences in permutations, 987

Labrande, Hugo. Computing Jacobi’s theta in quasi-linear time, 1479Landsberg, J. M. See Efremenko, Klim

Larson, Mats G. See Burman, Erik

Latche, J.-C. See Gallouet, T.Latche, J. C., and K. Saleh. A convergent staggered scheme for the variable density incompress-

ible Navier-Stokes equations, 581

Lee, Jeonghun J., and Ragnar Winther. Local coderivatives and approximation of Hodge Laplaceproblems, 2709

Lee, Yoonjin, and Yoon Kyung Park. A continued fraction of order twelve as a modular function,

2011Lehoucq, R. B., F. J. Narcowich, S. T. Rowe, and J. D. Ward. A meshless Galerkin method for

non-local diffusion using localized kernel bases, 2233

Li, Hengguang. An anisotropic finite element method on polyhedral domains: Interpolation erroranalysis, 1567

Li, Xiao. See Ju, LiliLichtman, Jared Duker, and Carl Pomerance. Improved error bounds for the Fermat primality

test on random inputs, 2871

Lim, Lek-Heng. See Friedland, ShmuelLinke, A., C. Merdon, M. Neilan, and F. Neumann. Quasi-optimality of a pressure-robust non-

conforming finite element method for the Stokes-problem, 1543

Liu, Hailiang, and Hairui Wen. Error estimates for the AEDG method to one-dimensional linearconvection-diffusion equations, 123

Liu, Jian-Guo. See Coquel, Frederic

Liu, Jian-Guo, Li Wang, and Zhennan Zhou. Positivity-preserving and asymptotic preservingmethod for 2D Keller-Segal equations, 1165

Lopez, L., and S. Maset. Time-transformations for the event location in discontinuous ODEs,2321

Lozano-Robledo, Alvaro. See Daniels, Harris B.. See Gonzalez-Jimenez, Enrique

Lu, Jianfeng, and Zhennan Zhou. Frozen Gaussian approximation with surface hopping for mixed

quantum-classical dynamics: A mathematical justification of fewest switches surface hop-

ping algorithms, 2189Luca, Florian. See Cilleruelo, Javier

Ma, Yunyun, and Yuesheng Xu. Computing highly oscillatory integrals, 309

Maas, Martın. See Acosta, GabrielMaltese, D. See Gallouet, T.

Martınez, J. M. See Birgin, E. G.

Martınez-Finkelshtein, A., A. Sri Ranga, and D. O. Veronese. Extreme zeros in a sequence ofpara-orthogonal polynomials and bounds for the support of the measure, 261

Mascot, Nicolas. Certification of modular Galois representations, 381Maset, S. See Lopez, L.

Massei, Stefano. See Bini, Dario A.

Mathe, Peter. See Plato, RobertMatthies, Gunar. See Franz, Sebastian

Meini, Beatrice. See Bini, Dario A.




































Melman, A. Eigenvalue bounds for matrix polynomials in generalized bases, 1935

Menares, Ricardo. See Burgos Gil, Jose Ignacio

Merdon, C. See Linke, A.Mezzarobba, Marc. See Chyzak, Frederic

Micheletti, Stefano. See Brugiapaglia, Simone

Moeller, Michael. See Bringmann, BjoernMolteni, Giuseppe. See Grenie, Loıc

Morini, Benedetta, Margherita Porcelli, and Philippe L. Toint. Approximate norm descent meth-

ods for constrained nonlinear systems, 1327Mustapha, Kassem. FEM for time-fractional diffusion equations, novel optimal error analyses,

2259

Najman, Filip. See Daniels, Harris B.Narcowich, F. J. See Hangelbroek, T.

. See Lehoucq, R. B.Neilan, M. See Linke, A.

Neumann, F. See Linke, A.

Neville, Stephen. See Rebenich, NikoNissen, Anna. See Wang, Siyang

Nobile, Fabio. See Brugiapaglia, Simone

Nogneng, Dorian, and Eric Schost. On the evaluation of some sparse polynomials, 893

Offner, Philipp. See Glaubitz, Jan

Oh, Duk-Soon, Olof B. Widlund, Stefano Zampini, and Clark R. Dohrmann. BDDC Algorithmswith deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector

fields, 659

Olshanskii, Maxim. See Guzman, JohnnyOlver, Sheehan. See Townsend, Alex

Ostergard, Patric R. J. See Kokkala, Janne I.

Park, Yoon Kyung. See Lee, YoonjinPerotto, Simona. See Brugiapaglia, Simone

Peterseim, Daniel. See Kornhuber, Ralf

Peyre, Gabriel. See Chizat, LenaıcPlato, Robert, Peter Mathe, and Bernd Hofmann. Optimal rates for Lavrentiev regularization

with adjoint source conditions, 785Pomerance, Carl. See Lichtman, Jared Duker

Poor, Cris. See King, Oliver D.

Porcelli, Margherita. See Morini, BenedettaPuppo, G. See Cravero, I.

Qiao, Zhonghua. See Ju, Lili

Qiu, Weifeng, Jiguang Shen, and Ke Shi. An HDG method for linear elasticity with strongsymmetric stresses, 69

Ramming, Tobias, and Holger Wendland. A kernel-based discretisation method for first order

partial differential equations, 1757Ranga, A. Sri. See Martınez-Finkelshtein, A.Rebenich, Niko, T. Aaron Gulliver, Stephen Neville, and Ulrich Speidel. An analog of the prime

number theorem for finite fields via truncated polylogarithm expansions, 855Rieder, Alexander. See Banjai, Lehel

Rieger, C. See Hangelbroek, T.Rivera-Letelier, Juan. See Burgos Gil, Jose Ignacio

Roop, J. P. See Ervin, V. J.Rowe, S. T. See Lehoucq, R. B.Rump, Siegfried M. See Jeannerod, Claude-PierreRuud, Hans Kristian. See Aanderaa, Stal

Sabawi, Younis A. See Cangiani, AndreaSaleh, K. See Latche, J. C.Sands, Jonathan W., and Brett A. Tangedal. Computing annihilators of class groups from

derivatives of L-functions, 2937Schenck, Hal. See Efremenko, Klim

Schmitzer, Bernhard. See Chizat, Lenaıc




















Schost, Eric. See Nogneng, Dorian

Schratz, Katharina. See Baumstark, Simon

Semplice, M. See Cravero, I.Shen, Jie. See Cai, Yongyong

Shen, Jiguang. See Qiu, Weifeng

Shen, Zuowei. See Han, BinShi, Ke. See Qiu, Weifeng

Shurman, Jerry. See King, Oliver D.

Siurys, J. See Drungilas, P.Sonar, Thomas. See Glaubitz, Jan

Speidel, Ulrich. See Rebenich, Niko

Stevenson, R. P. See Broersen, D.Stuart, Andrew M., and Aretha L. Teckentrup. Posterior consistency for Gaussian process ap-

proximations of Bayesian posterior distributions, 721Su, Chunmei. See Bao, Weizhu

Sutherland, Andrew V. See Daniels, Harris B.

Szpruch, Lukasz, and Xılıng Zhang. V -integrability, asymptotic stability and comparison prop-erty of explicit numerical schemes for non-linear SDEs, 755

Szymaszkiewicz, Lucjan. See D ↪abrowski, Andrzej

Tabata, Masahisa, and Shinya Uchiumi. An exactly computable Lagrange–Galerkin scheme forthe Navier–Stokes equations and its error estimates, 39

Tangedal, Brett A. See Sands, Jonathan W.

Teckentrup, Aretha L. See Stuart, Andrew M.Toint, Philippe L. See Morini, Benedetta

Townsend, Alex, Marcus Webb, and Sheehan Olver. Fast polynomial transforms based on Toeplitz

and Hankel matrices, 1913Tran, Hoang. See Chkifa, Abdellah

Trung, Ngo Viet. See Kemper, GregorTsai, Richard. See Kublik, Catherine

Uchiumi, Shinya. See Tabata, Masahisa

Van Anh, Nguyen Thi. See Kemper, GregorVeronese, D. O. See Martınez-Finkelshtein, A.

Vialard, Francois-Xavier. See Chizat, Lenaıc

Vinoles, Valentin. See Becache, Eliane

Visconti, G. See Cravero, I.

Wang, Chunmei, and Junping Wang. A primal-dual weak Galerkin finite element method forsecond order elliptic equations in non-divergence form, 515

Wang, Junping. See Wang, Chunmei

Wang, Li. See Coquel, Frederic. See Liu, Jian-Guo

Wang, Siyang, Anna Nissen, and Gunilla Kreiss. Convergence of finite difference methods for

the wave equation in two space dimensions, 2737Wang, Xiaojie. See Hutzenthaler, Martin

Ward, J. D. See Hangelbroek, T.. See Lehoucq, R. B.

Webb, Marcus. See Townsend, Alex

Webster, Clayton G. See Chkifa, AbdellahWen, Hairui. See Liu, HailiangWendland, Holger. See Ramming, Tobias

Weyman, Jerzy. See Efremenko, KlimWidlund, Olof B. See Oh, Duk-Soon

Wihler, Thomas P. See Houston, Paul

Williams, D. M. An entropy stable, hybridizable discontinuous Galerkin method for the com-pressible Navier-Stokes equations, 95

Winther, Ragnar. See Lee, Jeonghun J.

Wuthrich, Christian. Numerical modular symbols for elliptic curves, 2393Xia, Binzhou. Cyclotomic difference sets in finite fields, 2461

Xu, Yuesheng. See Ma, Yunyun


















Ye, Qiang. Accurate inverses for computing eigenvalues of extremely ill-conditioned matrices

and differential operators, 237

Yserentant, Harry. See Kornhuber, RalfYuan, Yongjun. See Cai, Yongyong

Yuen, David S. See King, Oliver D.

Zampini, Stefano. See Oh, Duk-SoonZhang, Hui. See Ju, Lili

Zhang, Jiwei. See Zhang, Qian

Zhang, Qian, Jiwei Zhang, Shidong Jiang, and Zhimin Zhang. Numerical solution to a linearizedtime fractional KdV equation on unbounded domains, 693

Zhang, Xılıng. See Szpruch, Lukasz

Zhang, Zhimin. See Zhang, QianZhou, Yang, and Xiaojun Chen. Spherical tε-designs for approximations on the sphere, 2831

Zhou, Zhennan. See Liu, Jian-Guo. See Lu, Jianfeng

Zhuang, Xiaosheng. See Han, Bin

Ziegler, Gunter M. See Brinkmann, PhilipZiegler, Volker. See Krenn, Daniel

Zimmer, C. See Altmann, R.






VOLUME 87 2018

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

Daniele BoffiSusanne C. Brenner, Managing EditorMartin BurgerAlbert CohenRonald F. A. CoolsBruno DespresQiang DuBettina EickHoward C. ElmanIvan GrahamRalf HiptmairMark van HoeijFrances KuoSven LeyfferChristian LubichGunter MalleAndrei Martınez-FinkelshteinJames McKeeMichael J. MossinghoffMichael J. NeilanFabio NobileAdam M. ObermanFrank-Olaf SchreyerChristoph SchwabZuowei ShenIgor E. ShparlinskiChi-Wang ShuAndrew V. SutherlandDaniel B. SzyldHans VolkmerBarbara Wohlmuth

Mathematics of Computation

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CONTENTS

Vol. 87, No. 309 January 2018

Simone Brugiapaglia, Fabio Nobile, Stefano Micheletti, and SimonaPerotto, A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Masahisa Tabata and Shinya Uchiumi, An exactly computableLagrange–Galerkin scheme for the Navier–Stokes equations and its errorestimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Weifeng Qiu, Jiguang Shen, and Ke Shi, An HDG method for linearelasticity with strong symmetric stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

D. M. Williams, An entropy stable, hybridizable discontinuous Galerkinmethod for the compressible Navier-Stokes equations . . . . . . . . . . . . . . . . . 95

Hailiang Liu and Hairui Wen, Error estimates for the AEDG method toone-dimensional linear convection-diffusion equations . . . . . . . . . . . . . . . . . 123

R. Altmann and C. Zimmer, Runge-Kutta methods for linear semi-explicitoperator differential-algebraic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

Jan Glaubitz, Philipp Offner, and Thomas Sonar, Application of modalfiltering to a spectral difference method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Steffen Borm, Adaptive compression of large vectors . . . . . . . . . . . . . . . . . . . . . 209

Qiang Ye, Accurate inverses for computing eigenvalues of extremelyill-conditioned matrices and differential operators . . . . . . . . . . . . . . . . . . . . . 237

A. Martınez-Finkelshtein, A. Sri Ranga, and D. O. Veronese,Extreme zeros in a sequence of para-orthogonal polynomials and boundsfor the support of the measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

Pedro Freitas, Sharp bounds for the modulus and phase of Hankel functionswith applications to Jaeger integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

Yunyun Ma and Yuesheng Xu, Computing highly oscillatory integrals . 309

Bin Han, Qingtang Jiang, Zuowei Shen, and Xiaosheng Zhuang,Symmetric canonical quincunx tight framelets with high vanishingmoments and smoothness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

Nicolas Mascot, Certification of modular Galois representations . . . . . . . . . 381

Harris B. Daniels, Alvaro Lozano-Robledo, Filip Najman, and An-drew V. Sutherland, Torsion subgroups of rational elliptic curves overthe compositum of all cubic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

Peter Bruin and Andrea Ferraguti, On L-functions of quadratic Q-curves 459

King Cheong Fung and Ben Kane, On sign changes of cusp forms and thehalting of an algorithm to construct a supersingular elliptic curve witha given endomorphism ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501

































Vol. 87, No. 310 March 2018

Chunmei Wang and Junping Wang, A primal-dual weak Galerkin finiteelement method for second order elliptic equations in non-divergenceform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515

Snorre H. Christiansen, On eigenmode approximation for Dirac equations:Differential forms and fractional Sobolev spaces . . . . . . . . . . . . . . . . . . . . . . 547

J. C. Latche and K. Saleh, A convergent staggered scheme for the variabledensity incompressible Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . 581

Erik Burman, Peter Hansbo, and Mats G. Larson, A cut finite elementmethod with boundary value correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633

Duk-Soon Oh, Olof B. Widlund, Stefano Zampini, and ClarkR. Dohrmann, BDDC Algorithms with deluxe scaling and adaptiveselection of primal constraints for Raviart-Thomas vector fields . . . . . . . 659

Qian Zhang, Jiwei Zhang, Shidong Jiang, and Zhimin Zhang,Numerical solution to a linearized time fractional KdV equation onunbounded domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693

Andrew M. Stuart and Aretha L. Teckentrup, Posterior consistency forGaussian process approximations of Bayesian posterior distributions . . 721

Lukasz Szpruch and Xılıng Zhang, V -integrability, asymptotic stabilityand comparison property of explicit numerical schemes for non-linearSDEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755

Robert Plato, Peter Mathe, and Bernd Hofmann, Optimal rates forLavrentiev regularization with adjoint source conditions . . . . . . . . . . . . . . 785

Claude-Pierre Jeannerod and Siegfried M. Rump, On relative errors offloating-point operations: Optimal bounds and applications . . . . . . . . . . . 803

Daniel Krenn and Volker Ziegler, Non-minimality of the width-w non-adjacent form in conjunction with trace one τ -adic digit expansions andKoblitz curves in characteristic two . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 821

Niko Rebenich, T. Aaron Gulliver, Stephen Neville, and UlrichSpeidel, An analog of the prime number theorem for finite fields viatruncated polylogarithm expansions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855

Oliver D. King, Cris Poor, Jerry Shurman, and David S. Yuen,Using Katsurada’s determination of the Eisenstein series to computeSiegel eigenforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879

Dorian Nogneng and Eric Schost, On the evaluation of some sparsepolynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893

Michael DiPasquale, Dimension of mixed splines on polytopal cells . . . . . . 905

Ruyong Feng, On the computation of the Galois group of linear differenceequations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 941

A. Detinko, D. L. Flannery, and A. Hulpke, Zariski density andcomputing in arithmetic groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 967

William Kuszmaul, Fast algorithms for finding pattern avoiders andcounting pattern occurrences in permutations . . . . . . . . . . . . . . . . . . . . . . . . 987

Greg Hurst, Computations of the Mertens function and improved bounds onthe Mertens conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1013









































Vol. 87, No. 311 May 2018

Erik Burman and Peter Hansbo, Stabilized nonconforming finite elementmethods for data assimilation in incompressible flows . . . . . . . . . . . . . . . . . 1029

D. Broersen, W. Dahmen, and R. P. Stevenson, On the stability ofDPG formulations of transport equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1051

Frederic Coquel, Shi Jin, Jian-Guo Liu, and Li Wang, Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm frontsampling for scalar conservation laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1083

T. Gallouet, R. Herbin, J.-C. Latche, and D. Maltese, Convergence ofthe MAC scheme for the compressible stationary Navier-Stokesequations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1127

Jian-Guo Liu, Li Wang, and Zhennan Zhou, Positivity-preserving andasymptotic preserving method for 2D Keller-Segal equations . . . . . . . . . . 1165

Yongyong Cai and Yongjun Yuan, Uniform error estimates of theconservative finite difference method for the Zakharov system in thesubsonic limit regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1191

Simon Baumstark, Erwan Faou, and Katharina Schratz, Uniformlyaccurate exponential-type integrators for Klein-Gordon equations withasymptotic convergence to the classical NLS splitting . . . . . . . . . . . . . . . . . 1227

Shmuel Friedland and Lek-Heng Lim, Nuclear norm of higher-ordertensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1255

Wanyou Cheng and Yu-Hong Dai, Gradient-based method with active setstrategy for `1 optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1283

E. G. Birgin, N. Krejic, and J. M. Martınez, On the employment ofinexact restoration for the minimization of functions whose evaluation issubject to errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1307

Benedetta Morini, Margherita Porcelli, and Philippe L. Toint,Approximate norm descent methods for constrained nonlinear systems 1327

Martin Hutzenthaler, Arnulf Jentzen, and Xiaojie Wang, Exponentialintegrability properties of numerical approximation processes fornonlinear stochastic differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1353

Abdellah Chkifa, Nick Dexter, Hoang Tran, and Clayton G.Webster, Polynomial approximation via compressed sensing of high-dimensional functions on lower sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1415

Laura Faber and Habiba Kadiri, Corrigendum to New bounds for ψ(x) 1451

Enrique Gonzalez-Jimenez and Alvaro Lozano-Robledo, On thetorsion of rational elliptic curves over quartic fields . . . . . . . . . . . . . . . . . . . 1457

Hugo Labrande, Computing Jacobi’s theta in quasi-linear time . . . . . . . . . . 1479

Andrzej D ↪abrowski and Lucjan Szymaszkiewicz, Orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves . . . . . . . 1509

P. Drungilas, J. Jankauskas, and J. Siurys, On Littlewood and Newmanpolynomial multiples of Borwein polynomials . . . . . . . . . . . . . . . . . . . . . . . . . 1523








































Vol. 87, No. 312 July 2018

A. Linke, C. Merdon, M. Neilan, and F. Neumann, Quasi-optimalityof a pressure-robust nonconforming finite element method for the Stokes-problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1543

Hengguang Li, An anisotropic finite element method on polyhedral domains:Interpolation error analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1567

Long Chen, Jun Hu, and Xuehai Huang, Fast auxiliary spacepreconditioners for linear elasticity in mixed form . . . . . . . . . . . . . . . . . . . . 1601

Martin J. Gander and Soheil Hajian, Analysis of Schwarz methods fora hybridizable discontinuous Galerkin discretization: The many-subdomain case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1635

Ruijian He, Xinlong Feng, and Zhangxin Chen, H1-Superconvergenceof a difference finite element method based on the P1 − P1-conformingelement on non-uniform meshes for the 3D Poisson equation . . . . . . . . . . 1659

I. Cravero, G. Puppo, M. Semplice, and G. Visconti, CWENO:Uniformly accurate reconstructions for balance laws . . . . . . . . . . . . . . . . . . 1689

Matt Elsey and Selim Esedoglu, Threshold dynamics for anisotropicsurface energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1721

Tobias Ramming and Holger Wendland, A kernel-based discretisationmethod for first order partial differential equations . . . . . . . . . . . . . . . . . . . 1757

Lehel Banjai and Alexander Rieder, Convolution quadrature for the waveequation with a nonlinear impedance boundary condition . . . . . . . . . . . . . 1783

Gabriel Acosta, Juan Pablo Borthagaray, Oscar Bruno, and MartınMaas, Regularity theory and high order numerical methods for the(1D)-fractional Laplacian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1821

Lili Ju, Xiao Li, Zhonghua Qiao, and Hui Zhang, Energy stability anderror estimates of exponential time differencing schemes for the epitaxialgrowth model without slope selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1859

Weizhang Huang and Lennard Kamenski, On the mesh nonsingularityof the moving mesh PDE method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1887

Alex Townsend, Marcus Webb, and Sheehan Olver, Fast polynomialtransforms based on Toeplitz and Hankel matrices . . . . . . . . . . . . . . . . . . . . 1913

A. Melman, Eigenvalue bounds for matrix polynomials in generalized bases 1935

T. Hangelbroek, F. J. Narcowich, C. Rieger, and J. D. Ward,An inverse theorem for compact Lipschitz regions in Rd using localizedkernel bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1949

Jan Buthe, An analytic method for bounding ψ(x) . . . . . . . . . . . . . . . . . . . . . . . 1991

Yoonjin Lee and Yoon Kyung Park, A continued fraction of order twelveas a modular function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2011

Klim Efremenko, J. M. Landsberg, Hal Schenck, and JerzyWeyman, The method of shifted partial derivatives cannot separatethe permanent from the determinant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2037

Zachary Charles, Generating random factored ideals in number fields . . . . 2047








































Vol. 87, No. 313 September 2018

Yongyong Cai and Jie Shen, Error estimates for a fully discretized schemeto a Cahn-Hilliard phase-field model for two-phase incompressible flows 2057

Johnny Guzman and Maxim Olshanskii, Inf-sup stability of geometri-cally unfitted Stokes finite elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2091

Sebastian Franz and Gunar Matthies, A unified framework for time-dependent singularly perturbed problems with discontinuous Galerkinmethods in time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2113

Weizhu Bao and Chunmei Su, Uniform error bounds of a finite differencemethod for the Klein-Gordon-Zakharov system in the subsonic limitregime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2133

Philippe Angot and Rima Cheaytou, On the error estimates of the vectorpenalty-projection methods: Second-order scheme . . . . . . . . . . . . . . . . . . . . 2159

Jianfeng Lu and Zhennan Zhou, Frozen Gaussian approximation withsurface hopping for mixed quantum-classical dynamics: A mathematicaljustification of fewest switches surface hopping algorithms . . . . . . . . . . . . 2189

R. B. Lehoucq, F. J. Narcowich, S. T. Rowe, and J. D. Ward, Ameshless Galerkin method for non-local diffusion using localized kernelbases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2233

Kassem Mustapha, FEM for time-fractional diffusion equations, noveloptimal error analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2259

V. J. Ervin, N. Heuer, and J. P. Roop, Regularity of the solution to 1-D fractional order diffusion equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2273

Yiannis Hadjimichael and David I. Ketcheson, Strong-stability-preserving additive linear multistep methods . . . . . . . . . . . . . . . . . . . . . . . . . 2295

L. Lopez and S. Maset, Time-transformations for the event location indiscontinuous ODEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2321

Bjoern Bringmann, Daniel Cremers, Felix Krahmer, and MichaelMoeller, The homotopy method revisited: Computing solution pathsof `1-regularized problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2343

Catherine Kublik and Richard Tsai, An extrapolative approach tointegration over hypersurfaces in the level set framework . . . . . . . . . . . . . 2365

Christian Wuthrich, Numerical modular symbols for elliptic curves . . . . . . 2393

Jose Ignacio Burgos Gil, Ricardo Menares, and Juan Rivera-Letelier, On the essential minimum of Faltings’ height . . . . . . . . . . . . . . . 2425

Binzhou Xia, Cyclotomic difference sets in finite fields . . . . . . . . . . . . . . . . . . . 2461

Loıc Grenie and Giuseppe Molteni, Explicit bounds for generators of theclass group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2483

Gregor Kemper, Ngo Viet Trung, and Nguyen Thi Van Anh, Towarda theory of monomial preorders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2513

Maria Bras-Amoros and Julio Fernandez-Gonzalez, Computation ofnumerical semigroups by means of seeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2539

Janne I. Kokkala and Patric R. J. Ostergard, The chromatic number ofthe square of the 8-cube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2551











































Lenaıc Chizat, Gabriel Peyre, Bernhard Schmitzer, and Francois-Xavier Vialard, Scaling algorithms for unbalanced optimal transportproblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2563

Christian Kreuzer and Emmanuil H. Georgoulis, Convergence ofadaptive discontinuous Galerkin methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2611

Paul Houston and Thomas P. Wihler, An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear ellipticboundary value problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2641





Eliane Becache, Patrick Joly, and Valentin Vinoles, On the analysis ofperfectly matched layers for a class of dispersive media and applicationto negative index metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2775

Dario A. Bini, Stefano Massei, and Beatrice Meini, Semi-infinite quasi-Toeplitz matrices with applications to QBD stochastic processes . . . . . . 2811

Yang Zhou and Xiaojun Chen, Spherical tε-designs for approximations onthe sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2831

Zhijian He, Quasi-Monte Carlo for discontinuous integrands withsingularities along the boundary of the unit cube . . . . . . . . . . . . . . . . . . . . . 2857

Jared Duker Lichtman and Carl Pomerance, Improved error bounds forthe Fermat primality test on random inputs . . . . . . . . . . . . . . . . . . . . . . . . . . 2871


Stal Aanderaa, Lars Kristiansen, and Hans Kristian Ruud, Search forgood examples of Hall’s conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2903

Markus Hittmeir, A babystep-giantstep method for faster deterministicinteger factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2915



Frederic Chyzak, Thomas Dreyfus, Philippe Dumas, and MarcMezzarobba, Computing solutions of linear Mahler equations . . . . . . . 2977

Javier Cilleruelo, Florian Luca, and Lewis Baxter, Every positiveinteger is a sum of three palindromes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3023







































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Editorial Committee

SUSANNE C. BRENNER, Chair, Center for Computation & Technology and Depart-ment of Mathematics, Louisiana State University, Baton Rouge, LA 70803 USA;E-mail : [email protected]

IGOR E. SHPARLINSKI, Department of Pure Mathematics, University of New SouthWales, Sydney, NSW 2052, Australia; E-mail : [email protected]

CHI-WANG SHU, Applied Mathematics Division, Brown University, P.O. Box F, 182George St., Providence, RI 02912-0001 USA; E-mail : [email protected]

DANIEL B. SZYLD, Department of Mathematics 038-16, Temple University, 638Wachman, 1805 N. Broad St. Philadelphia, PA 19122-6094 USA; E-mail : [email protected]

Board of Associate Editors

DANIELE BOFFI, Department of Mathematics, University di Pavia, Via Ferrata 1,27100 Pavia PV, Italy; E-mail : [email protected]

MARTIN BURGER, Institut fur Numerische und Angewandte Mathematik, West-faelisch Wilhelms-Universitat Munster, Einsteinstr. 62, D-48149 Munster, Germany;E-mail : [email protected]

ALBERT COHEN, Laboratoire Jacques-Louis Lions, Universite Pierre et Marie Curie,4, Place Jussieu, 75005 Paris, France; E-mail : [email protected]

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

kuleuven.ac.be

BRUNO DESPRES, University of Paris VI, Laboratory Jacques-Louis Lions, 175 ruedu Chevaleret, 75013 Paris, France; E-mail : [email protected]

QIANG DU, Columbia University, 500 W 120th Street, APAM, 200 Mudd, MC 4701,New York, NY 10027, USA; E-mail : [email protected]

BETTINA EICK, Institut Computational Mathematics, University of Braunschweig,38106 Braunschweig, Germany; E-mail : [email protected]

HOWARD C. ELMAN, Department of Computer Science, University of Maryland,College Park, MD 20742 USA; E-mail : [email protected]

IVAN G. GRAHAM, Department of Mathematical Sciences, University of Bath, BathBA2 7AY, United Kingdom; E-mail : [email protected]

RALF HIPTMAIR, Department of Mathematics, Seminar of Applied Mathematics,ETH Zurich, CH-8092 Zurich, Switzerland. E-mail : [email protected]

MARK van HOEIJ, Department of Mathematics, Florida State University, 1017 Aca-demic Way, Tallahassee, FL 32306 USA; E-mail : [email protected]

FRANCES KUO, University of New South Wales, School of Mathematics, SydneyNSW 2052, Australia; E-mail : [email protected]

SVEN LEYFFER, Mathematics and Computer Science Division, Argonne NationalLaboratory, Argonne, IL 60439, USA; E-mail : [email protected]

CHRISTIAN LUBICH, Mathematisches Institut, Universitat Tubingen, Auf der Mor-genstelle 10, 72076 Tubingen, Germany; E-mail : [email protected]

GUNTERMALLE, Fachbereich Mathematik, Universitat Kaiserslautern, Postfach 3049,67653 Kaiserslautern, Germany; E-mail : [email protected]

ANDREI MARTINEZ-FINKELSHTEIN, Department of Mathematics, Baylor Univer-sity, Waco, TX 76798 USA; and Department of Mathematics, University of Almeria, 04120Almeria, Spain; E-mail : a [email protected]

JAMES MCKEE, Department of Mathematics, Royal Holloway University of London,Egham Hill, Egham TW20 0EX, United Kingdom; E-mail : [email protected]

MICHAEL J. MOSSINGHOFF, Department of Mathematics, Davidson College, Box6996, Davidson, NC 28035-6996 USA; E-mail : [email protected]

MICHAEL J. NEILAN, Department of Mathematics, University of Pittsburgh, Pitts-burgh, PA 15260 USA; E-mail : [email protected]

FABIO NOBILE, Mathematics Institute of Computational Science and Engineering,

Ecole Polytechnique Federale de Lausanne, CH 1015 Lausanne, Switzerland; E-mail :[email protected]

ADAM M. OBERMAN, Department of Mathematics and Statistics, McGill University,805 Sherbrooke St W, Montreal QC H3A 0B9, Canada; E-mail : [email protected]

FRANK-OLAF SCHREYER, Faculty of Mathematics and Computer Science, SaarlandUniversity, Campus E2 4, 66123 Saarbrucken, Germany; E-mail : [email protected]

CHRISTOPH SCHWAB, Seminar for Applied Mathematics, ETH Zurich, Raemistrasse101, HG G57.1, CH-8092 Zurich, Switzerland; E-mail : [email protected]

ZUOWEI SHEN, Department of Mathematics, National University of Singapore, BlockS17 10, Lower Kent Ridge Road, 119076 Singapore; E-mail : [email protected]

ANDREW V. SUTHERLAND, Department of Mathematics, Massachusetts Instituteof Technology, Cambridge, MA 02139 USA; E-mail : [email protected]

HANS VOLKMER, Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201-0413 USA; E-mail : [email protected]

BARBARAWOHLMUTH, Fakultat fur Mathematik, Technische Universitat Munchen,Boltzmannstr. 3, 85748 Garching, Germany; E-mail : [email protected]

(Continued from back cover)


Frederic Chyzak, Thomas Dreyfus, Philippe Dumas, and MarcMezzarobba, Computing solutions of linear Mahler equations . . . . . . 2977

Javier Cilleruelo, Florian Luca, and Lewis Baxter, Every positiveinteger is a sum of three palindromes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3023







CONTENTS


Lenaıc Chizat, Gabriel Peyre, Bernhard Schmitzer, and Francois-Xavier Vialard, Scaling algorithms for unbalanced optimal transportproblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2563

Christian Kreuzer and Emmanuil H. Georgoulis, Convergence ofadaptive discontinuous Galerkin methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2611

Paul Houston and Thomas P. Wihler, An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear ellipticboundary value problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2641





Eliane Becache, Patrick Joly, and Valentin Vinoles, On the analysis ofperfectly matched layers for a class of dispersive media and applicationto negative index metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2775

Dario A. Bini, Stefano Massei, and Beatrice Meini, Semi-infinite quasi-Toeplitz matrices with applications to QBD stochastic processes . . . . . 2811

Yang Zhou and Xiaojun Chen, Spherical tε-designs for approximationson the sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2831

Zhijian He, Quasi-Monte Carlo for discontinuous integrands withsingularities along the boundary of the unit cube . . . . . . . . . . . . . . . . . . . . 2857

Jared Duker Lichtman and Carl Pomerance, Improved error boundsfor the Fermat primality test on random inputs . . . . . . . . . . . . . . . . . . . . . . 2871


Stal Aanderaa, Lars Kristiansen, and Hans Kristian Ruud, Searchfor good examples of Hall’s conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2903

Markus Hittmeir, A babystep-giantstep method for faster deterministicinteger factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2915


(Continued on inside back cover)

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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 · volume 87 (2018) are as follows: for paper...

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