【作者】 张新东；

【导师】 张知难；

【作者基本信息】 新疆大学 ， 计算数学， 2008， 硕士

【摘要】 本文主要研究了两个方面的内容:线性约束下双反对称矩阵扩充及其最佳逼近;矩阵方程AX = B的双反对称最佳逼近解.本文首次研究了关于矩阵方程AX = B的双反对称问题.在讨论线性约束下双反对称矩阵扩充及其最佳逼近时,给出以下两个问题并对其进行讨论得到相关定理:问题1给定求A∈BASR^n×n,使得问题2给定A^*∈R^n×n,求A|^∈S₁,使得,其中S1是问题1的解集合.在讨论矩阵方程AX = B的双反对称最佳逼近解时,给出以下两个问题并对其进行讨论得到相关定理:问题3给定A∈R^k×n, B∈R^k×n,求X∈BASR^n×n,使得AX = B.问题4给定X^*∈R^n×n,求X∈S₃,使得,其中S3是问题3的解集合.最后,总结了本文的研究工作,并对该课题有待进一步研究的工作进行了展望.更多还原

【Abstract】 In this paper, we consider two problems, the expansion of anti-bisymmetric matrix andits optimal approximation with the linear constraint and the anti-bisymmetric optimalapproximation solution of matrix equation AX = B. In this paper, the anti-bisymmetricmatrices problem of matrix equation AX = B was researched for the first time.When we consider the expansion of anti-bisymmetric and its optimal approximationwith the linear constraint, we discuss the following problems and get two theorems:Problem 1Given X, B∈Rn×k and A0∈ASRq×q, find A∈BASRn×n, such thatProblem 2Given A~*∈Rn×n, find A∈S1 such thatwhere S1 is the solution set of Problem 1.When we consider the anti-bisymmetric optimal approximation solution of matrixequation AX = B, we discuss the following problems and get two theorems:Problem 3Given A, B∈Rk×n, find X∈BASRn×n, such thatAX = B.Problem 4Given X?∈Rn×n, find X∈S3 such thatwhere S3 is the solution set of Problem 3.At the end, we make a work summary of this paper and look forward to the followingresearch work about this subject.更多还原