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INVERSE PROBLEMS and REGULARIZATION THEORY – Part II

Every restriction corresponds to a law of nature, a regularization of the universe. Carl Sagan. INVERSE PROBLEMS and REGULARIZATION THEORY – Part II. AIP 2011 Texas A&M University MAY 22, 2011. CHUCK GROETSCH. OUTLINE. What is Regularization?.

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INVERSE PROBLEMS and REGULARIZATION THEORY – Part II

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

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

  3. REGULARIZATION

  4. Tikhonov Regularization

  5. Compact Operators K

  6. Discrepancy Principle

  7. Variational Characterization

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

  9. RTSVD

  10. RTSVD

  11. RTSVD

  12. RTSVD

  13. Finite Elements

  14. Finite Rank - Quadrature

  15. Finite Rank - Quadrature

  16. Iterated Tikhonov Regularization

  17. Iterative Regularization

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