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矩阵方程XA＋YB=C的对称次反对称解及最佳逼近
  • ISSN号：1006-6330
  • 期刊名称：《应用数学与计算数学学报》
  • 时间：0
  • 分类：O151.21[理学—数学;理学—基础数学]
  • 作者机构：[1]湖州师范学院理学院,浙江湖州313000
  • 相关基金：国家自然科学基金资助项目（11071079）; 浙江省自然科学基金资助项目（Y6110043）; 安徽高校省级科研重点资助项目（KJ2013A204）
作者： 丰雅萍[1], 蔡静[1]
关键词： 矩阵方程, 对称次反对称解, 矩阵分解, 最佳逼近, matrix equation, symmetric and skew anti-symmetric solution, matrix decomposition, optimal approximation
中文摘要：

探讨了矩阵方程XA＋YB=C存在对称次反对称解的条件及解的表达式.利用矩阵分解,给出了方程有解的充要条件和解的解析表达式.在矩阵方程的解集合中,利用Frobenius-矩阵范数正交不变性获得了给定矩阵的最佳逼近解的表达式,并建立了相应的数值算法.

英文摘要：

The conditions for the matrix equation XA ＋ YB = C to have a symmetric and skew anti-symmetric solution and its expression are discussed.Based on the matrix decomposition,the necessary and sufficient conditions for the existence of a solution are given.In the solution set of the above equation,by using orthogonal invariance of the Probenius norm,the expression of optimal approximation solution to a given matrix is derived.Moreover,the corresponding numerical algorithm is presented.

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期刊信息
  • 《应用数学与计算数学学报》
  • 主管单位:上海市教育委员会
  • 主办单位:上海大学
  • 主编：马和平
  • 地址：上海市上大路99号121信箱上海大学期刊社
  • 邮编：200444
  • 邮箱：camc@oa.shu.edu.cn
  • 电话：021-66137602
  • 国际标准刊号：ISSN：1006-6330
  • 国内统一刊号：ISSN：31-1436/O1
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘
  • 被引量:1282