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一类高维线性Hankel-循环矩阵的PROCRUSTES问题

发表时间:2018-10-15  浏览量:125  下载量:35
全部作者: 文亚云,邓远北,宋晓燕
作者单位: 湖南大学数学与计量经济学院
摘 要: 研究在Hankel-循环矩阵X的约束下,高维线性矩阵方程组ArXBr=Cr(r=1,2,•••,m)的最小二乘问题。利用循环矩阵的性质,结合最优化原理,将其转化为线性方程Qy=b的求解问题,获得了通解的表达式。当A1, A2,•••, Ap, Bp+1,•••, Bm为置换矩阵时,证明了Q是一个特殊循环对称矩阵,并给出了唯一解的条件及表达式,同时借助矩阵的m1-范数,获得了具有唯一解的相关判定条件。最后,给出了具体算法和数值算例。
关 键 词: 计算数学;Hankel-循环矩阵;高维矩阵方程组;最小二乘问题;对称矩阵
Title: A class of PROCRUSTES problem for high-dimensional linear Hankel-circular matrices
Author: WEN Yayun, DENG Yuanbei, SONG Xiaoyan
Organization: College of Mathematics and Econometrices, Hunan University
Abstract: An efficient method based on the properties of circulant matrices and the optimization theory is used to solve the least squares problem of high-dimensional linear matrix equations ArXBr=Cr (r=1,2,•••,m) over the constraint of Hankel-circular matrices X. The general expression of the solution is given by the linear equation Qy=b derived from the matrix equations. When A1, A2,•••, Ap, Bp+1,•••, Bm are permutation matrices, it is proved that Q is a special symmetric circulant matrix. The determination condition of the unique solution and its expression is derived. The relevant condition with unique solutions is obtained by the m1-norm of the matrices. Finally, results of numerical experiments are given.
Key words: computational mathematics; Hankel-circular matrices; high-dimensional matrix equations; the least squares problem; symmetric matrix
发表期数: 2018年10月第19期
引用格式: 文亚云,邓远北,宋晓燕. 一类高维线性Hankel-循环矩阵的PROCRUSTES问题[J]. 中国科技论文在线精品论文,2018,11(19):1914-1926.
 
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