title: New algorithms to compute the nearness symmetric solution of the matrix equation.
abstract: In this paper we consider the nearness symmetric solution of the matrix equation AXB = C to a given matrix [Formula: see text] in the sense of the Frobenius norm. By discussing equivalent form of the considered problem, we derive some necessary and sufficient conditions for the matrix [Formula: see text] is a solution of the considered problem. Based on the idea of the alternating variable minimization with multiplier method, we propose two iterative methods to compute the solution of the considered problem, and analyze the global convergence results of the proposed algorithms. Numerical results illustrate the proposed methods are more effective than the existing two methods proposed in Peng et al. (Appl Math Comput 160:763-777, 2005) and Peng (Int J Comput Math 87: 1820-1830, 2010).
authors.affiliation: School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, 541004 Guangxi China.
authors.forename: Zhen-Yun
authors.initials: ZY
authors.lastname: Peng
authors.affiliation: School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, 541004 Guangxi China.
authors.forename: Yang-Zhi
authors.initials: YZ
authors.lastname: Fang
authors.affiliation: School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, 541004 Guangxi China.
authors.forename: Xian-Wei
authors.initials: XW
authors.lastname: Xiao
authors.affiliation: School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, 541004 Guangxi China.
authors.forename: Dan-Dan
authors.initials: DD
authors.lastname: Du
keywords: AVMM method; Iteration method; Matrix equation; Matrix nearness problem; Symmetric matrix