Thesis--Auburn University, 2009. / Abstract. Vita. Includes bibliographic references (p.50-52).

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

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

Thesis (Ph.D.)--City University of Hong Kong, 2009. / "Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [52]-58)

Thesis (Ph. D.)--University of Hong Kong, 1993.

A generalized Conjugate Gradient like method is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. Preconditioning techniques are employed with the Conjugate Gradient like method to enhance the stability and convergence rate of the overall iterative method. The superiority of the new solver is established by comparisons with a conventional Line GaussSeidel Relaxation (LGSR) solver. Comparisons are based on 'number of iterations required to converge to a steady-state solution' and 'total CPU time required for convergence'. Three test cases representing widely varying flow physics are chosen to investigate the performance of the solvers. Computational test results for very low speed (incompressible flow over a backward facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (shockon- shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the 1vfach 0.1 case, speed-up factors of 30 (in terms of iterations) and 20 (in terms of CPU time) are found in favor of the new solver when compared with the LGSR solver. The corresponding speed-up factors for the transonic flow case are 20 and 18, respectively. The hypersonic case shows relatively lower speed-up factors of 5 and 4, respectively. This study reveals that preconditioning can greatly enhance the range of applicability and improve the performance of Conjugate Gradient like methods. / Ph. D.

Kwok-po Ng. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 138-139). / Abstracts / Summary / Introduction --- p.1 / Summary of the papers A-F --- p.2 / Paper A --- p.15 / Paper B --- p.36 / Paper C --- p.63 / Paper D --- p.87 / Paper E --- p.109 / Paper F --- p.122

by Wun-Cheung Tang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references. / Abstract also in Chinese. / Abstracts --- p.1 / Introduction --- p.3 / Toeplitz and Circulant Matrices --- p.3 / Conjugate Gradient Method --- p.6 / Cosine Transform Preconditioner --- p.7 / Regularization --- p.10 / Summary --- p.13 / Paper A --- p.19 / Paper B --- p.36

Thesis (M.S.)--Brigham Young University. Dept. of Mechanical Engineering, 2003. / Includes bibliographical references (p. 87-89).

Thesis (Ph.D.)--University of Tulsa, 1993. / Includes bibliographical references (leaves 254-269).