1. 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

2. OUTLINE What is Regularization? Tikhonov Regularization Iterative Regularization Convergence Theory Role of the SVD Discretizations Iterated T-regularization Landweber Iteration

3. REGULARIZATION

4. Tikhonov Regularization

5. Compact Operators K

7. Discrepancy Principle

8. Variational Characterization

9. The Regularization Dance Approximation Error: Discretization Error: Stability Error:

10. RTSVD

14. Finite Elements

15. Finite Rank - Quadrature

17. Iterated Tikhonov Regularization

18. Iterative Regularization