On iterative refinement/improvement of the solution to an ill conditioned linear system.

Title: On iterative refinement/improvement of the solution to an ill conditioned linear system.
Identifier: AAI3308679
identifier: 3308679
Creator: Serme, Abdramane.
Contributor: Adviser: Victor Y. Pan
Date: 2008
Language: English
Publisher: City University of New York.
Subject: Mathematics | Computer Science
Abstract: We study additive preconditioning A → C = A + UVH for preconditioner UVH of a smaller rank r. The SMW formula A-1 = ( C -- UVH)-1 = C-1 + C-1 U(Ir -- VHC -1U)-1V HC-1 reduces the solution of a linear system Ax = b to better conditioned linear systems with the matrices S = Ir -- VHC-1U and C. The computations preserve the structure and the sparseness of the input matrix A. We compute the matrix W = C-1U with a higher precision by applying iterative refinement/improvement to approximate the matrix W closely as a sum W0+W 1+...+Wk, where the matrices W i are filled with low precision values.;We prove that if C-1Fk 1-C-1Fk < 1, where Fk = Ck -- C, Xk = W0 + ... + Wk and X = W , then Xk-X ≤Ou . By applying forward error analysis, we prove that Xk-X X ≤Ou , and by applying backward error analysis that limk→infinity Uk-CWk &dvbm0;C&dvbm0;&dvbm0;Wk&dvbm0; =4c1k 1-c'1k cond2Cuu&d1; , where c1(k) and c'1k are linear functions in k.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.

Media: On iterative refinement/improvement of the solution to an ill conditioned linear system.