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On the Hermitian Positive Definite Solutions of the Nonlinear Matrix Equation X^s -A^＊X^-tA = Q with Perturbation Estimates
  • ISSN号：2095-2651
  • 期刊名称：《数学研究及应用：英文版》
  • 时间：0
  • 分类：O151.21[理学—数学;理学—基础数学] O241.6[理学—计算数学;理学—数学]
  • 作者机构：[1]School of Science, Huzhou Teachers College, Zhejiang 313000, P. R. China
  • 相关基金：Supported by the National Natural Science Foundation of China （Grant No. 11071079） and the Natural Science Foundation of Zhejiang Province （Grant No. Y6110043）.
作者： Jing CAI[1]
关键词： HERMITE正定解, 非线性矩阵方程, 扰动估计, 埃尔米特, 解的存在性, 正定矩阵, 条件方程, 正整数, matrix equation, Hermitian positive definite solution, property, existence, perturbation bound.
中文摘要：

In this paper,the Hermitian positive definite solutions of the nonlinear matrix equation Xs A X tA = Q are studied,where Q is a Hermitian positive definite matrix,s and t are positive integers.The existence of a Hermitian positive definite solution is proved.A sufcient condition for the equation to have a unique Hermitian positive definite solution is given.Some estimates of the Hermitian positive definite solutions are obtained.Moreover,two perturbation bounds for the Hermitian positive definite solutions are derived and the results are illustrated by some numerical examples.

英文摘要：

In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^＊X^-tA = Q are studied, where Q is a Hermitian positive definite matrix, s and t are positive integers. The existence of a Hermitian positive definite solution is proved. A sufficient condition for the equation to have a unique Hermitian positive definite solution is given. Some estimates of the Hermitian positive definite solutions are obtained. Moreover, two perturbation bounds for the Hermitian positive definite solutions are derived and the results are illustrated by some numerical examples.

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期刊信息
  • 《数学研究及应用：英文版》
  • 中国科技核心期刊
  • 主管单位:国家教育部
  • 主办单位:大连理工大学
  • 主编：王仁宏
  • 地址：大连理工大学应用数学系
  • 邮编：116024
  • 邮箱：
  • 电话：0411-84707392
  • 国际标准刊号：ISSN：2095-2651
  • 国内统一刊号：ISSN：21-1579/O1
  • 邮发代号:8-92
  • 获奖情况:
  • 1998年大连市优秀期刊奖,2000年大连市优秀期刊奖
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊
  • 被引量:36