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反对称偏对称矩阵反问题的最小二乘解
  • ISSN号：0254-3079
  • 期刊名称：应用数学学报
  • 时间：0
  • 页码：221-231
  • 分类：O211.4[理学—概率论与数理统计;理学—数学]
  • 作者机构：[1]广东工业大学应用数学学院,广州510520, [2]华南师范大学数学科学学院,广州510631
  • 相关基金：国家自然科学基金（10671077 10971075）; 广东省自然科学基金（06025061 9151063101000021）; 广东工业大学校级博士启动基金（103005）资助项目
  • 相关项目：基因概率布尔网络模型的数值分析
作者： 莫荣华|黎稳|
关键词： 反对称矩阵, 偏对称矩阵, 反问题, 最小二乘解, 最佳逼近, anti-symmetric matrix, persymmetric matrix, inverse problem, least-squares solution, best approximation
中文摘要：

该文研究了反对称偏对称矩阵反问题的最小二乘解,得到了该问题解的表达式以及该问题有解的充分必要条件.证明了其最佳逼近解的存在性和唯一性,建立了其最佳逼近解的表达式,并给出了求最佳逼近解的数值算法和算例.

英文摘要：

In this paper the authors mainly discuss the least-squares solutions of inverse problem for anti-symmetric and persymmetric matrices.The necessary and sufficient condition of solvability for the problem are conducted.And the general form of solutions is presented.Further,the authors study the optimal approximation solution to any given matrix, prove that such solution is unique and provide the formula to compute it.A numerical examples is given to demonstrate that the results are right and the algorithm is feasible.

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期刊信息
  • 《应用数学学报》
  • 中国科技核心期刊
  • 主管单位:中国科学院
  • 主办单位:中国数学会 中国科学院数学与系统科学研究院
  • 主编：丁夏畦
  • 地址：北京市海淀区中关村东路55号
  • 邮编：100190
  • 邮箱：
  • 电话：
  • 国际标准刊号：ISSN：0254-3079
  • 国内统一刊号：ISSN：11-2040/O1
  • 邮发代号:2-822
  • 获奖情况:
  • 1996、2000年获“中科院优秀科技期刊”三等奖,1997年获“第二届全国优秀科技期刊”三等奖,2001年入选“双效期刊”（中国期刊方阵）
  • 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,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:6864