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求一类矩阵方程组的最小二乘行对称解及其最佳逼近的迭代法 被引量：1

An Iterative Method for the Least Squares Row Symmetric Solution of a Class of the Matrix Equations and Its Optimal Approximation
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摘要 本文构造了求矩阵方程组AX=B,XC=D的最小二乘行对称解及其最佳逼近的迭代法,研究了迭代序列的性质,证明了算法的收敛性。 In this paper,an algorithm is constructed to solve the least squares row symmetric solution of the matrix equations AX=B,XC=D and its optimal approximation.Some properties of the iterative sequence have been derived,and the method has been shown to preserve convergence properties.
作者 胡荣 张磊
机构地区 湖南大学
出处 《数学理论与应用》 2010年第4期118-121,共4页 Mathematical Theory and Applications
基金 国家自然科学基金资助项目(No.10571047)资助
关键词 迭代法 梯度矩阵 行对称解 Algorithm Gradient matrix Row symmetric solution
分类号 O241.6 [理学—计算数学]
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参考文献4

  • 1Mitra S K. The matrix equations AX = B, XB = D [J]. Linear Algebra Appl. , 1984, 59,171 -181.
  • 2Li F. L. , Hu X. Y. and Zhang L. The generalized reflexive solution for a class of matrix equations ( AX= B, XC = D) [ J ]. Acta Mathematica Scientia, 2008, 28B ( 1 ), 185 - 193.
  • 3Li F. L. , Hu X. Y. and Zhang L. Least - squares mirrosymmetric solution for matrix equations ( AX = B, XC = D ) [ J ]. Numerical Mathematics A Journal of Chinese Universities ( English series ), 2006,15 ( 3 ), 217 - 226.
  • 4彭卓华,胡锡炎,张磊.求矩阵方程组A_1XB_1=C_1,A_2XB_2=C_2最小二乘对称解及其最佳逼近的迭代法[J].湘潭大学自然科学学报,2007,29(2):13-19. 被引量：3

二级参考文献11

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数学理论与应用
2010年 第4期

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