关于病态线性方程组条件预优的若干讨论  

ON THE PRECONDITION OF ILL-CONDITIONED SYSTEM OF LINEAR EQUATIONS

作　　者：罗亮生[1] 

机构地区：[1]南京大学

出　　处：《高等学校计算数学学报》1989年第4期369-372,共4页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(1860451)

摘　　要：众所周知,病态线性方程组 Ax=b(1)的预优方程组 BAx=Bb (2)的预优效果与B的选取密切相关。本文将指出,预优效果同采用什么种类的浮点运算、数组A、b能否在计算机上精确表示出来以及方程组的规模也有很大关系。 讨论中,我们假定计算机的字长为二进制t位,浮点运算符号fl(·)和fl_2(·)的含义同J.H.Wilkinson.x.表示(1)的精确解,δz表示z的扰动量。此外,为简单计,假定文中涉及到的矩阵都是n阶非异方阵,向量都是n维的;·是1-范数或∞-It is well known that the preconditioned efficiency of replacing the ill-conditioned system of linear equations Ax = b by the preconditioned system BAx = Bb is closely associated with the choice of matrix B. Besides, in this paper we indicate that it is also associated with the kind of the floating point arithmetic used in machine , the size of the system of linear equations and whether the arrays A, b can be represented exactly within computer.

关 键 词：病态 线性方程组 预优方程组 

分 类 号：O241.6[理学—计算数学]