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