一类矩阵方程中心对称解的可信性验证  

Credibility Verification of Centrosymmetric Solutions of a Class of Matrix Equations

作　　者：桑海风[1] 李敏[1] 刘畔畔[1] 李庆春[1] SANG Haifeng LI Min LIU Panpan LI Qingchun(College of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin Province, China)

机构地区：[1]北华大学数学与统计学院,吉林吉林132013

出　　处：《吉林大学学报（理学版）》2017年第5期1135-1140,共6页Journal of Jilin University:Science Edition

基　　金：吉林省教育厅科学技术研究项目(批准号:2015131;2015156;JJKH20170022KJ)

摘　　要：考虑矩阵方程AXB+BXA=C(A,B,C,X∈C^(n×n))中心对称解的可信性验证问题.在A,B可同时对角化的假设下,提出一种区间算法,该算法输出一个近似中心对称解及其相应的误差界,使得在近似解的误差范围内必存在该方程的一个精确中心对称解,且该算法的复杂度仅为O(n^3).We considered credibility verification of centrosymmetric solutions of matrix equation AXB＋BXA=C（A,B,C,X∈C^n×n）.Under the assumption of simultaneous diagonalization of Aand B,we proposed an interval algorithm that output an approximate centrosymmetric solution and its corresponding error bound,so that an exact centrosymmetric solution of the equation must exist in the error range of the approximate solution,and the complexity of the algorithm was only O（n^3）.

关 键 词：矩阵方程 中心对称矩阵 可信性验证 区间 

分 类 号：O242.29[理学—计算数学]