臺灣博碩士論文加值系統

本文是作解線性系統 Ax=b 數值解的研究, 其中 A 是一個維度為 N;對
稱; 正定; 大而且疏鬆的矩陣. 我們考慮用預設條件化共軛梯度法
(preconditioned conjugate gradient method) 來求解. 當務之急, 是
要先選定好預設條件化矩陣 (preconditioned matrix). 在本文中, 介紹
一般常用的預設條件化子包括不完全 LU 分解法 (incomplete LU
ation), 不完全 Cholesky 分解法 (incomplete cholesky, 還有對稱連
續超鬆弛法 (SSOR method). 同時也載述預設條件化子的理論結果. 文中
並附有數值結果而且利用結果進一步討論預設條件化共軛梯度法的影響.

Numerical solutions of the system of liner algebraic equation=
b, where A is an n*n symmetric positive definite large
andmatrix, are studied. The method considered are theconjugate
gradient methods. Various choices of the preconditioned matrix
associated with matrix A, including SSor,complete LU
factorization and incomplete cholesky factorizatione
introduced. Theoretical results associated with theseoned are
presented. Numerical results and discussionstness of the
preconditioned conjugate gradientso be illustrated.