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 ...