INVERSE PROBLEMS and REGULARIZATION THEORY – Part II AIP 2011 Texas A&M University MAY 22, 2011 CHUCK GROETSCH Every restriction corresponds to a law of.

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INVERSE PROBLEMS and REGULARIZATION THEORY – Part II AIP 2011 Texas 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

Finite Elements

Finite Rank - Quadrature

Iterated Tikhonov Regularization

Iterative Regularization