一类广义Stein方程的正定解

段雪峰1,2,王卿文2,常海霞3

doi:10.3969/j.issn.1007-2861.2012.01.005

上海大学学报(自然科学版) >

2012 , Vol. 18 >Issue 1: 26 - 29

DOI: https://doi.org/10.3969/j.issn.1007-2861.2012.01.005

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一类广义Stein方程的正定解

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1.桂林电子科技大学数学与计算科学学院,广西桂林 541004; 2.上海大学理学院,上海 200444;3.上海金融学院应用数学系,上海 201209

收稿日期: 2010-09-03

网络出版日期: 2012-02-29

基金资助

国家自然科学基金资助项目（11101100,71101033）；广西自然科学基金资助项目（0991238）

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Positive Definite Solution for a Class of Generalized Stein Equation

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1. College of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, Guangxi, China;2. College of Sciences, Shanghai University, Shanghai 200444, China;3. Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, China

Received date: 2010-09-03

Online published: 2012-02-29

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摘要

基于Thompson度量的良好性质,给出一类广义Stein方程存在正定解的充分条件;构造求解的迭代方法,并给出该迭代方法的误差估计式;最后用数值例子验证了该迭代方法的可行性.

关键词： 迭代方法; 广义Stein方程; 误差估计; 正定解

本文引用格式

段雪峰1,2,王卿文2,常海霞3 . 一类广义Stein方程的正定解[J]. 上海大学学报(自然科学版), 2012 , 18(1) : 26 -29 . DOI: 10.3969/j.issn.1007-2861.2012.01.005

Abstract

Based on the elegant properties of the Thompson metric, we give a sufficient condition for the existence of positive definite solution for a class of generalized Stein equation. An iterative method is proposed to compute the positive definite solution, and its error estimate formula is also derived. Numerical examples show that this iterative method is feasible.

Key words： error estimate; generalized Stein equation; iterative method; positive definite solution

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