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Inverse problems: ill-posedness, error estimates and numerical experiments.

Wang Yuliang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 70-75). / Abstracts in English and Chinese. / Chapter 1 --- Introduction to Inverse Problems --- p.1 / Chapter 1.1 --- Typical Examples --- p.1 / Chapter 1.2 --- Major Properties --- p.3 / Chapter 1.3 --- Solution Methods --- p.4 / Chapter 1.4 --- Thesis Outline --- p.4 / Chapter 2 --- Review of the Theory --- p.6 / Chapter 2.1 --- Basic Concepts --- p.6 / Chapter 2.1.1 --- Ill-posedness --- p.6 / Chapter 2.1.2 --- Generalized Inverse --- p.7 / Chapter 2.1.3 --- Compact Operators and SVE --- p.8 / Chapter 2.2 --- Regularization Methods --- p.10 / Chapter 2.2.1 --- An Overview --- p.11 / Chapter 2.2.2 --- Convergence Rates --- p.12 / Chapter 2.2.3 --- Parameter Choice Rules --- p.15 / Chapter 2.2.4 --- Classical Regularization Methods --- p.18 / Chapter 3 --- Ill-posedenss of Typical Inverse Problems --- p.23 / Chapter 3.1 --- Integral Equations --- p.24 / Chapter 3.2 --- Inverse Source Problems --- p.26 / Chapter 3.3 --- Parameter Identification --- p.34 / Chapter 3.4 --- Backward Heat Conduction --- p.37 / Chapter 4 --- Error Estimates for Parameter Identification --- p.39 / Chapter 4.1 --- Overview of Numerical Methods --- p.40 / Chapter 4.2 --- Finite Element Spaces and Standard Estimates --- p.43 / Chapter 4.3 --- Output Least-square Methods --- p.43 / Chapter 4.4 --- Equation Error Methods --- p.50 / Chapter 4.5 --- Hybrid Methods --- p.50 / Chapter 5 --- Numerical Experiments --- p.52 / Chapter 5.1 --- Formulate the Linear Systems --- p.53 / Chapter 5.2 --- Test Problems and Observations --- p.55 / Bibliography --- p.70

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_325690
Date January 2006
ContributorsWang, Yuliang., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, ii, 75 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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