APPROXIMATION OF MATRIX-VALUED FUNCTIONS

被引：18
|
作者：
MATHIAS, R
机构：
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1993年 / 14卷 / 04期
关键词：
MATRIX-VALUED FUNCTION; TRUNCATED TAYLOR SERIES; NUMERICAL INTEGRATION;
D O I：
10.1137/0614070
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is shown that if f(z) = SIGMA(i=0)infinity a(i)z(i) (the series having radius of convergence R) then for any n x n matrix A with spectral radius less than R and any norm \\.\\ on the space of n x n matrices [GRAPHICS] It is also shown that expressions for the error in numerical integration rules can be generalized to matrix-valued functions. The main point of the paper is that in these two cases it is not necessary to increase the bound by a factor depending on n when generalizing an inequality for scalar-valued functions to n x n matrix-valued functions.
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页码：1061 / 1063
页数：3
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