‖A-1‖∞的上界和等对角优势

计算物理 ›› 1991, Vol. 8 ›› Issue (1): 68-78.

‖A^-1‖_∞的上界和等对角优势

胡家赣

北京应用物理与计算数学研究所, 100088

收稿日期:1989-12-15 出版日期:1991-03-25 发布日期:1991-03-25

UPPER BOUND OF ‖A^-1‖_∞ AND EQUIDIAGONAL DOMINANCE

Hu Jiagan

Institute of Applied Physics and Computatinal Mathematics 100088

Received:1989-12-15 Online:1991-03-25 Published:1991-03-25

摘要/Abstract

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|a₁₁-||a₁₁|=δ,∀_i),则ρ(A^-1)=‖A^-1‖_x=(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。

关键词: 等对角优势矩阵, 对角优势矩阵, 逆矩阵的最大模

Abstract: 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-dominanceδ|i.e.|a₁₁-||a₁₁|=δ,∀_i),则ρ(A^-1)=‖A^-1‖_x=(A^-1)_ij=1/δ,∀_i, By use of equidiagonal-dominant matrix the upper bound of ‖A^-1‖_x for any H-matrx may be found. Several interesting examples are given to illustrate our theorems.

Key words: equidiagonal dominant matrix, diagonal dominant matrix, maximum norm of inverse matrix

胡家赣. ‖A^-1‖_∞的上界和等对角优势[J]. 计算物理, 1991, 8(1): 68-78.

Hu Jiagan. UPPER BOUND OF ‖A^-1‖_∞ AND EQUIDIAGONAL DOMINANCE[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1991, 8(1): 68-78.