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Performance investigation of some existing numerical methods for inverse problems.

Cheung, Man Wah. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 89-91). / Abstracts in English and Chinese. / Chapter 1 --- Introduction to Inverse Problems --- p.1 / Chapter 1.1 --- Major properties --- p.1 / Chapter 1.2 --- Typical examples --- p.3 / Chapter 1.3 --- Thesis outline --- p.5 / Chapter 2 --- Some Operator Theory --- p.6 / Chapter 2.1 --- Fredholm integral equation of the first kind --- p.6 / Chapter 2.2 --- Compact operator theory --- p.8 / Chapter 2.3 --- Singular system --- p.12 / Chapter 2.4 --- Moore-Penrose generalized inverse --- p.14 / Chapter 3 --- Regularization Theory for First Kind Equations --- p.19 / Chapter 3.1 --- General regularization theory --- p.19 / Chapter 3.2 --- Tikhonov regularization --- p.24 / Chapter 3.3 --- Landweber iteration --- p.26 / Chapter 3.4 --- TSVD --- p.28 / Chapter 4 --- Multilevel Algorithms for Ill-posed Problems --- p.30 / Chapter 4.1 --- Basic assumptions and definitions --- p.31 / Chapter 4.2 --- Multilevel analysis --- p.33 / Chapter 4.3 --- Applications --- p.37 / Chapter 4.3.1 --- Preconditioned iterative methods with nonzero regularization parameter --- p.38 / Chapter 4.3.2 --- Preconditioned iterative methods with zero regularization parameter --- p.38 / Chapter 4.3.3 --- Full multilevel algorithm --- p.40 / Chapter 5 --- Numerical Experiments --- p.41 / Chapter 5.1 --- Integral equations --- p.41 / Chapter 5.1.1 --- Discretization --- p.42 / Chapter 5.1.2 --- Test problems --- p.43 / Chapter 5.1.3 --- "Singular values, singular vectors and condition numbers" --- p.45 / Chapter 5.1.4 --- Effect of condition numbers on numerical accuracies --- p.49 / Chapter 5.2 --- Differential equations --- p.50 / Chapter 5.2.1 --- Discretization --- p.51 / Chapter 5.2.2 --- "Singular values, singular vectors and condition numbers" --- p.53 / Chapter 5.3 --- Numerical experiments by classical methods --- p.55 / Chapter 5.3.1 --- Tikhonov regularization --- p.55 / Chapter 5.3.2 --- TSVD --- p.56 / Chapter 5.3.3 --- Landweber iteration --- p.63 / Chapter 5.4 --- Numerical experiments by multilevel methods --- p.63 / Chapter 5.4.1 --- General convergence --- p.63 / Chapter 5.4.2 --- Numerical results --- p.65 / Chapter 5.4.3 --- Effect of multilevel parameters on convergence --- p.76 / Bibliography --- p.89

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326104
Date January 2007
ContributorsCheung, Man Wah., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, viii, 91 leaves : ill. ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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