Thesis (Ph. D.)--University of Washington, 1996. / Vita. Includes bibliographical references (leaves [58]-60).

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

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (leaves [86]-88).

Chan Yuet Tai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 107-111). / Chapter 1 --- Introduction to Sturm-Liouville Problem --- p.1 / Chapter 1.1 --- What are inverse problems? --- p.1 / Chapter 1.2 --- Introductory background --- p.2 / Chapter 1.3 --- The Liouville transformation --- p.3 / Chapter 1.4 --- The Sturm-Liouville problem 一 A historical look --- p.4 / Chapter 1.5 --- Where Sturm-Liouville problems come from? --- p.6 / Chapter 1.6 --- Inverse problems of interest --- p.8 / Chapter 2 --- Reconstruction Method I --- p.10 / Chapter 2.1 --- Perturbative inversion --- p.10 / Chapter 2.1.1 --- Inversion problem via Fredholm integral equation --- p.10 / Chapter 2.1.2 --- Output least squares method for ill-posed integral equations --- p.15 / Chapter 2.1.3 --- Numerical experiments --- p.17 / Chapter 2.2 --- Total inversion --- p.38 / Chapter 2.3 --- Summary --- p.45 / Chapter 3 --- Reconstruction Method II --- p.46 / Chapter 3.1 --- Computation of q --- p.47 / Chapter 3.2 --- Computation of the Cauchy data --- p.48 / Chapter 3.2.1 --- Recovery of Cauchy data for K --- p.51 / Chapter 3.2.2 --- Numerical implementation for computation of the Cauchy data . --- p.51 / Chapter 3.3 --- Recovery of q from Cauchy data --- p.52 / Chapter 3.4 --- Iterative procedure --- p.53 / Chapter 3.5 --- Numerical experiments --- p.60 / Chapter 3.5.1 --- Eigenvalues without noised data --- p.64 / Chapter 3.5.2 --- Eigenvalues with noised data --- p.69 / Chapter 4 --- Appendices --- p.79 / Chapter A --- Tikhonov regularization --- p.79 / Chapter B --- Basic properties of the Sturm-Liouville operator --- p.80 / Chapter C --- Asymptotic formulas for the eigenvalues --- p.86 / Chapter C.1 --- Case 1: h ≠ ∞ and H ≠ ∞ --- p.87 / Chapter C.2 --- Case 2: h= ∞ and H ≠∞ --- p.90 / Chapter C.3 --- Case 3: h = ∞ and H = ∞ --- p.91 / Chapter D --- Completeness of the eigenvalues --- p.92 / Chapter E --- d'Alembert solution formula for the wave equation --- p.97 / Chapter E.1 --- "The homogeneous solution uH(x,t)" --- p.98 / Chapter E.2 --- "The particular solution up(x, t)" --- p.99 / Chapter E.3 --- "The standard d'Alembert solution u(x,t)" --- p.101 / Chapter E.4 --- Applications to our problem --- p.101 / Chapter F --- Runge-Kutta method for solving eigenvalue problems --- p.104 / Bibliography --- p.107

Lee Wai Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 129-130). / Text in English; abstract also in Chinese. / Lee Wai Shing. / Contents --- p.i / List of Figures --- p.v / Abstract --- p.vii / Acknowledgement --- p.ix / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- What are inverse problems? --- p.1 / Chapter 1.2 --- Background of this research project --- p.2 / Chapter 1.3 --- Conservative systems and open systems -normal modes (NM's) vs quasi-normal modes (QNM's) --- p.3 / Chapter 1.4 --- Appetizer ´ؤ What our problems are like --- p.6 / Chapter 1.5 --- A brief overview of the following chapters --- p.7 / Chapter Chapter 2. --- Inversion of conservative systems- perturbative inversion --- p.9 / Chapter 2.1 --- Overview --- p.9 / Chapter 2.2 --- Way to introduce the additional information --- p.9 / Chapter 2.3 --- General Formalism --- p.11 / Chapter 2.4 --- Example --- p.15 / Chapter 2.5 --- Further examples --- p.19 / Chapter 2.6 --- Effects of noise --- p.23 / Chapter 2.7 --- Conclusion --- p.25 / Chapter Chapter 3. --- Inversion of conservative systems - total inversion --- p.26 / Chapter 3.1 --- Overview --- p.26 / Chapter 3.2 --- Asymptotic behaviour of the eigenfrequencies --- p.26 / Chapter 3.3 --- General formalism --- p.28 / Chapter 3.3.1 --- Evaluation of V(0) --- p.28 / Chapter 3.3.2 --- Squeezing the interval - evaluation of the potential at other positions --- p.32 / Chapter 3.4 --- Remarks --- p.36 / Chapter 3.5 --- Conclusion --- p.37 / Chapter Chapter 4. --- Theory of Quasi-normal Modes (QNM's) --- p.38 / Chapter 4.1 --- Overview --- p.38 / Chapter 4.2 --- What is a Quasi-normal Mode (QNM) system? --- p.38 / Chapter 4.3 --- Properties of QNM's in expectation --- p.40 / Chapter 4.4 --- General Formalism --- p.41 / Chapter 4.4.1 --- Construction of Green's function and the spectral represen- tation of the delta function --- p.42 / Chapter 4.4.2 --- The generalized norm --- p.45 / Chapter 4.4.3 --- Completeness of QNM's and its justification --- p.46 / Chapter 4.4.4 --- Different senses of completeness --- p.48 / Chapter 4.4.5 --- Eigenfunction expansions with QNM's 一 the two-component formalism --- p.49 / Chapter 4.4.6 --- Properties of the linear space Γ --- p.51 / Chapter 4.4.7 --- Klein-Gordon equation - The delta-potential system --- p.54 / Chapter 4.5 --- Studies of other QNM systems --- p.54 / Chapter 4.5.1 --- Wave equation - dielectric rod --- p.55 / Chapter 4.5.2 --- Wave equation ´ؤ string-mass system --- p.57 / Chapter 4.6 --- Summary --- p.58 / Chapter Chapter 5. --- Inversion of open systems- perturbative inversion --- p.59 / Chapter 5.1 --- Overview --- p.59 / Chapter 5.2 --- General Formalism --- p.59 / Chapter 5.3 --- Example 1. Klein-Gordon equation ´ؤ delta-potential system --- p.66 / Chapter 5.3.1 --- Model perturbations --- p.66 / Chapter 5.4 --- Example 2. Wave equation ´ؤ dielectric rod --- p.72 / Chapter 5.5 --- Example 3. Wave equation ´ؤ string-mass system --- p.76 / Chapter 5.5.1 --- Instability of the matrix [d] = [c]-1 upon truncation --- p.79 / Chapter 5.6 --- Large leakage regime and effects of noise --- p.81 / Chapter 5.7 --- Conclusion . . . --- p.84 / Chapter Chapter 6. --- Transition from open systems to conservative counterparts --- p.85 / Chapter 6.1 --- Overview --- p.85 / Chapter 6.2 --- Anticipations of what is going to happen --- p.86 / Chapter 6.3 --- Some computational experiments --- p.86 / Chapter 6.4 --- Reason of breakdown - An intrinsic error of physical systems --- p.87 / Chapter 6.4.1 --- Mathematical derivation of the breakdown behaviour --- p.90 / Chapter 6.4.2 --- Two verifications --- p.93 / Chapter 6.5 --- Another source of errors - An intrinsic error of practical computations --- p.95 / Chapter 6.5.1 --- Vindications --- p.96 / Chapter 6.5.2 --- Mathematical derivation of the breakdown --- p.98 / Chapter 6.6 --- Further sources of errors --- p.99 / Chapter 6.7 --- Dielectric rod --- p.100 / Chapter 6.8 --- String-mass system --- p.103 / Chapter 6.9 --- Conclusion --- p.105 / Chapter Chapter 7. --- A first step to Total Inversion of QNM systems? --- p.106 / Chapter 7.1 --- Overview --- p.106 / Chapter 7.2 --- Derivation for F(0) --- p.106 / Chapter 7.3 --- Example 一 delta potential system --- p.108 / Chapter Chapter 8. --- Conclusion --- p.111 / Chapter 8.1 --- A summary on what have been achieved --- p.111 / Chapter 8.2 --- Further directions to go --- p.111 / Appendix A. A note on notation --- p.113 / Appendix B. Asymptotic series of NM eigenvalues --- p.114 / Appendix C. Evaluation of functions related to RHS(x) --- p.117 / Appendix D. Asymptotic behaviour of the Green's function --- p.119 / Appendix E. Expansion coefficient an --- p.121 / Appendix F. Asymptotic behaviour of QNM eigenvalues --- p.123 / Appendix G. Properties of the inverse matrix [d] = [c]-1 --- p.125 / Appendix H. Matrix inverse through the LU decomposition method --- p.127 / Bibliography --- p.129

Hung Kin Ting. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 126-129). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Inverse Problems --- p.1 / Chapter 1.2 --- Applications of Inverse Problems --- p.2 / Chapter 1.3 --- Least-squares Solutions --- p.4 / Chapter 1.4 --- Discrete Systems --- p.4 / Chapter 1.5 --- "Discretization, Regularization and Regularization Pa- rameters" --- p.5 / Chapter 1.6 --- Outline of the Thesis --- p.6 / Chapter 2 --- Some Basic Concepts and Mathematical Tools --- p.8 / Chapter 2.1 --- Singular Value Decomposition (SVD) --- p.8 / Chapter 2.2 --- Generalized Singular Value Decomposition (GSVD) --- p.13 / Chapter 2.3 --- White Noises --- p.16 / Chapter 3 --- Regularized Solutions --- p.18 / Chapter 3.1 --- Derivation of Regularized Solutions --- p.18 / Chapter 3.2 --- Discrete Picard Condition --- p.20 / Chapter 3.3 --- Relationship between Discrete Picard Condition and Regularized Solution --- p.21 / Chapter 3.4 --- Checking for the Discrete Picard Condition --- p.22 / Chapter 4 --- Different Discretization Approaches --- p.23 / Chapter 4.1 --- Problem 1 - Volterra Integral Equation of the First Kind --- p.25 / Chapter 4.2 --- Examples of Problem 1 --- p.30 / Chapter 4.3 --- Problem 2 - Fredholm Integral Equation of the First Kind --- p.49 / Chapter 4.4 --- Examples of Problem 2 --- p.53 / Chapter 4.5 --- Conclusion --- p.57 / Chapter 5 --- Effect of Different Kinds of Observation Data and Differential Operators on Accuracy --- p.59 / Chapter 5.1 --- Pointwise Observation Data --- p.60 / Chapter 5.2 --- Pointwise Observation Data of Heat Fluxes at the Boundary --- p.69 / Chapter 5.3 --- Observation Data with Heat Fluxes --- p.80 / Chapter 5.4 --- Conclusion --- p.89 / Chapter 6 --- L-curve --- p.90 / Chapter 6.1 --- Properties of L-curve --- p.93 / Chapter 6.2 --- L-curve in Log-Log Scale --- p.100 / Chapter 6.3 --- Disadvantages of the L-curve Method --- p.100 / Chapter 7 --- Algorithms of Finding the Corner of L-curve --- p.105 / Chapter 7.1 --- Cubic Spline Curve Fitting --- p.105 / Chapter 7.2 --- Conic Section Fitting --- p.106 / Chapter 7.3 --- Triangle Method --- p.109 / Chapter 8 --- Implementation of the L-curve Method --- p.111 / Chapter 8.1 --- Our Algorithm --- p.111 / Chapter 8.2 --- Numerical Experiments --- p.112 / Chapter 8.3 --- Conclusion --- p.124 / Bibliography --- p.126

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

Thesis (M.S.)--Ohio University, June, 2000. / Title from PDF t.p.

Thesis (Ph. D.)--University of Washington, 2008. / Vita. Includes bibliographical references (p. 99-102).

Thesis (Ph. D.)--University of Washington, 1993. / Vita. Includes bibliographical references (leaves [54]-55).