INVERSE PROBLEMS and REGULARIZATION THEORY – Part II
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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 o nature, a regularization of the universe. Carl Saga
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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?. - PowerPoint PPT Presentation
Transcript of 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
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OUTLINE
What is Regularization?
Tikhonov Regularization
Iterative Regularization
Convergence Theory
Role of the SVD
Discretizations
Iterated T-regularization
Landweber Iteration
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REGULARIZATION
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Tikhonov Regularization
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Compact Operators K
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Discrepancy Principle
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Variational Characterization
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The Regularization Dance
Approximation Error:
Discretization Error:
Stability Error:
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RTSVD
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RTSVD
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RTSVD
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RTSVD
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Finite Elements
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Finite Rank - Quadrature
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Finite Rank - Quadrature
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Iterated Tikhonov Regularization
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Iterative Regularization
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