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

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.viList of Figures --- p.viiChapter 1 --- Solving Systems of ODEs with BVMs --- p.1Chapter 1.1 --- Introduction --- p.1Chapter 1.2 --- Background --- p.4Chapter 1.2.1 --- Linear Multistep Formulae --- p.4Chapter 1.2.2 --- Preconditioned GMRES Method --- p.6Chapter 1.3 --- Strang-Type Preconditioners with BVMs --- p.7Chapter 1.3.1 --- Block-BVMs and Their Matrix Forms --- p.8Chapter 1.3.2 --- Construction of the Strang-type Preconditioner --- p.10Chapter 1.3.3 --- Convergence Rate and Operation Cost --- p.12Chapter 1.3.4 --- Numerical Result --- p.13Chapter 1.4 --- Strang-Type BCCB Preconditioner --- p.15Chapter 1.4.1 --- Construction of BCCB Preconditioners --- p.15Chapter 1.4.2 --- Convergence Rate and Operation Cost --- p.17Chapter 1.4.3 --- Numerical Result --- p.19Chapter 1.5 --- Preconditioned Waveform Relaxation --- p.20Chapter 1.5.1 --- Waveform Relaxation --- p.20Chapter 1.5.2 --- Invertibility of the Strang-type preconditioners --- p.23Chapter 1.5.3 --- Convergence rate and operation cost --- p.24Chapter 1.5.4 --- Numerical Result --- p.25Chapter 1.6 --- Multigrid Waveform Relaxation --- p.27Chapter 1.6.1 --- Multigrid Method --- p.27Chapter 1.6.2 --- Numerical Result --- p.28Chapter 1.6.3 --- Concluding Remark --- p.30Chapter 2 --- Restoration of Chopped and Nodded Images --- p.31Chapter 2.1 --- Introduction --- p.31Chapter 2.2 --- The Projected Landweber Method --- p.35Chapter 2.3 --- Other Numerical Methods --- p.37Chapter 2.3.1 --- Tikhonov Regularization --- p.38Chapter 2.3.2 --- MRNSD --- p.41Chapter 2.3.3 --- Piecewise Polynomial TSVD --- p.43Chapter 2.4 --- Numerical Result --- p.46Chapter 2.5 --- Concluding Remark --- p.47Bibliography --- p.4