Circulant preconditioners from B-splines and their applications.

by Tat-Ming Tso.Thesis (M.Phil.)--Chinese University of Hong Kong, 1997.Includes bibliographical references (p. 43-45).Chapter Chapter 1 --- INTRODUCTION --- p.1Chapter §1.1 --- Introduction --- p.1Chapter §1.2 --- Preconditioned Conjugate Gradient Method --- p.3Chapter §1.3 --- Outline of Thesis --- p.3Chapter Chapter 2 --- CIRCULANT AND NON-CIRCULANT PRECONDITIONERS --- p.5Chapter §2.1 --- Circulant Matrix --- p.5Chapter §2.2 --- Circulant Preconditioners --- p.6Chapter §2.3 --- Circulant Preconditioners from Kernel Function --- p.8Chapter §2.4 --- Non-circulant Band-Toeplitz Preconditioners --- p.9Chapter Chapter 3 --- B-SPLINES --- p.11Chapter §3.1 --- Introduction --- p.11Chapter §3.2 --- New Version of B-splines --- p.15Chapter Chapter 4 --- CIRCULANT PRECONDITIONERS CONSTRUCTED FROM B-SPLINES --- p.24Chapter Chapter 5 --- NUMERICAL RESULTS AND CONCLUDING REMARKS --- p.28Chapter Chapter 6 --- APPLICATIONS TO SIGNAL PROCESSING --- p.37Chapter §6.1 --- Introduction --- p.37Chapter §6.2 --- Preconditioned regularized least squares --- p.39Chapter §6.3 --- Numerical Example --- p.40REFERENCES --- p.4