Numerical methods for solving systems of ODEs with BVMs and restoration of chopped and nodded images.

• Other Authors: Tam, Yue Hung.
• Format: Others
• Language: English; Chinese
• Published: 2002
• Subjects: Boundary value problems > Numerical solutions; Initial value problems > Numerical solutions; Inverse problems (Differential equations); Multigrid methods (Numerical analysis)
• Online Access: http://library.cuhk.edu.hk/record=b5891191; http://repository.lib.cuhk.edu.hk/en/item/cuhk-324102

by Tam Yue Hung. === Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. === Includes bibliographical references (leaves 49-52). === Abstracts in English and Chinese. === List of Tables --- p.vi === List of Figures --- p.vii === Chapter 1 --- Solving Systems of ODEs with BVMs --- p.1 === Chapter 1.1 --- Introduction --- p.1 === Chapter 1.2 --- Background --- p.4 === Chapter 1.2.1 --- Linear Multistep Formulae --- p.4 === Chapter 1.2.2 --- Preconditioned GMRES Method --- p.6 === Chapter 1.3 --- Strang-Type Preconditioners with BVMs --- p.7 === Chapter 1.3.1 --- Block-BVMs and Their Matrix Forms --- p.8 === Chapter 1.3.2 --- Construction of the Strang-type Preconditioner --- p.10 === Chapter 1.3.3 --- Convergence Rate and Operation Cost --- p.12 === Chapter 1.3.4 --- Numerical Result --- p.13 === Chapter 1.4 --- Strang-Type BCCB Preconditioner --- p.15 === Chapter 1.4.1 --- Construction of BCCB Preconditioners --- p.15 === Chapter 1.4.2 --- Convergence Rate and Operation Cost --- p.17 === Chapter 1.4.3 --- Numerical Result --- p.19 === Chapter 1.5 --- Preconditioned Waveform Relaxation --- p.20 === Chapter 1.5.1 --- Waveform Relaxation --- p.20 === Chapter 1.5.2 --- Invertibility of the Strang-type preconditioners --- p.23 === Chapter 1.5.3 --- Convergence rate and operation cost --- p.24 === Chapter 1.5.4 --- Numerical Result --- p.25 === Chapter 1.6 --- Multigrid Waveform Relaxation --- p.27 === Chapter 1.6.1 --- Multigrid Method --- p.27 === Chapter 1.6.2 --- Numerical Result --- p.28 === Chapter 1.6.3 --- Concluding Remark --- p.30 === Chapter 2 --- Restoration of Chopped and Nodded Images --- p.31 === Chapter 2.1 --- Introduction --- p.31 === Chapter 2.2 --- The Projected Landweber Method --- p.35 === Chapter 2.3 --- Other Numerical Methods --- p.37 === Chapter 2.3.1 --- Tikhonov Regularization --- p.38 === Chapter 2.3.2 --- MRNSD --- p.41 === Chapter 2.3.3 --- Piecewise Polynomial TSVD --- p.43 === Chapter 2.4 --- Numerical Result --- p.46 === Chapter 2.5 --- Concluding Remark --- p.47 === Bibliography --- p.49