加权范数下矩阵方程组的对称解及其最佳逼近

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

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

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

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/Abstract

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

钟青，孙合明，胡珊珊. 加权范数下矩阵方程组的对称解及其最佳逼近[J]. 计算机工程与应用, 2011, 47(9): 45-47.

ZHONG Qing，SUN Heming，HU Shanshan. Symmetric solution with weighted norm for matrix equations and their optimal approximation[J]. Computer Engineering and Applications, 2011, 47(9): 45-47.