【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（n³）.更多还原

【Abstract】 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（n³）.更多还原