摘要
本文在A为H阵的情况下给出了一个较前人给出的更为简单和具体的‖A^(-1)‖_x的上界,本文还定义了“等对角优势矩阵”,并证明了若A为具有等对角优势δ的等对角优势矩阵(亦即|α_(ij)|-sum from i≠1 to(|α_(ij)|)=δ,(?)_i),则P(A^(-1))=‖A^(-1)‖_x=sum from j to(A^(-1))_(ij)=1/δ,(?)_i,利用等对角优势M阵,可以求任何H阵A的‖A^(-1)‖_x的上界,最后我们还给出了几个有趣的例子以说明本文的一些定理。
A simpler and more concrete estimate of the upper bound of ||A-1|| than those in previous papers is given, when A is an H-matrix and the equidiagonal dominant matrix is defined.We prove that if A is an equidiagonal-dominant M-matrix with equidiagonal-dominance, then , Vi, By use of equidiagonal-dominant matrix the upper bound of for any H-matrx may be found. Several interesting examples are given to illustrate our theorems.
出处
《计算物理》
CSCD
北大核心
1991年第1期68-78,共11页
Chinese Journal of Computational Physics
关键词
等对角优势
矩阵
对角优势
逆矩阵
equidiagonal dominant matrix, diagonal dominant matrix, maximum norm of inverse matrix.
