计算机工程与应用 ›› 2011, Vol. 47 ›› Issue (9): 45-47.

• 研究、探讨 • 上一篇    下一篇

加权范数下矩阵方程组的对称解及其最佳逼近

钟 青,孙合明,胡珊珊   

  1. 河海大学 理学院,南京 210098
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2011-03-21 发布日期:2011-03-21

Symmetric solution with weighted norm for matrix equations and their optimal approximation

ZHONG Qing,SUN Heming,HU Shanshan   

  1. The College of Science,Hohai University,Nanjing 210098,China
  • Received:1900-01-01 Revised:1900-01-01 Online:2011-03-21 Published:2011-03-21

摘要: 应用复合最速下降法,给出了求解矩阵方程组[(AXB=E,CXD=F)]加权范数下对称解及最佳逼近问题的迭代解法。对任意给定的初始矩阵,该迭代算法能够在有限步迭代计算之后得到矩阵方程组的对称解,并且在上述解集合中也可给出指定矩阵的最佳逼近矩阵。

关键词: 复合最速下降法, 矩阵方程组, 对称解, 加权Frobenius范数, 最佳逼近

Abstract: Based on the hybrid steepest descent method,an iterative method for the symmetric solution and optimal approximation solution of matrix equations [(AXB=E,CXD=F)] with weighted norm is derived.For any initial matrix,a symmetric solution can be obtained within finite iteration steps in the absence of round-off errors.In addition,the related optimal approximation problem to a given matrix over the solution set is solved.

Key words: the hybrid steepest descent method, matrix equations, symmetric solution, weighted Frobenius norm, optimal approximation