粗格子校正预条件共轭梯度法  

CONJUGATE GRADIENT METHOD WITH PRECONDITIONING BY COARSE-GRID CORRECTION OPERATOR

作　　者：曹志浩[1] 黄德所[1] 徐卫[1] 

机构地区：[1]复旦大学

出　　处：《高等学校计算数学学报》1993年第2期128-137,共10页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金;国家攀登项目资助课题

摘　　要：预条件共轭梯度法是求解大型线性方程组的一类非常有效的方法,文[5]和[8]从不同的出发点导出了求解对称正定线性方程组的相同的预条件共轭梯度法(他们分别称之为投影预条件共轭梯度法和收缩残量共轭梯度法)。 本文从多格子方法的观点出发导出这类预条件共轭梯度法,并推广到求解对称正半定奇异线性组。最后详细讨论构成粗格子预条件算子的限制矩阵的取法,并估计相应的条件数。A method for improving the convergence of the standard conjugate gradient method is given. The method involves using the coarse-grid correction operator as preconditioner and can be used to solve the symmetric positive definite system of equations as well as the symmetric positive semi-definite singular system of equations. The convergence of the method is discussed and the upper bounds of the condition numbers of the preconditioned matrices for some restriction matrices, which determine the coarse-grid operators, are given.

关 键 词：共轭梯度法 线性方程组 多格子法 

分 类 号：O241.6[理学—计算数学]