inverse problems and regularization theory – part ii
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INVERSE PROBLEMS and REGULARIZATION THEORY – Part II
AIP 2011Texas A&M University
MAY 22, 2011
CHUCK GROETSCH
Every restriction corresponds to a law of nature,a regularization of the universe.
Carl Sagan
OUTLINE
What is Regularization?
Tikhonov Regularization
Iterative Regularization
Convergence Theory
Role of the SVD
Discretizations
Iterated T-regularization
Landweber Iteration
REGULARIZATION
Tikhonov Regularization
Compact Operators K
Discrepancy Principle
Variational Characterization
The Regularization Dance
Approximation Error:
Discretization Error:
Stability Error:
RTSVD
RTSVD
RTSVD
RTSVD
Finite Elements
Finite Rank - Quadrature
Finite Rank - Quadrature
Iterated Tikhonov Regularization
Iterative Regularization
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