A numerical method on the mixed solution of matrix equation ∑i=1tAiXiBi=E with sub-matrix constraints and its application

Hongli Qu, Dongxiu Xie and Jie Xu

Applied Mathematics and Computation, 2021, vol. 411, issue C

Abstract: We put forward and analyze in details an iterative method to find the mixed solutions of a matrix equation with sub-matrix constraints. The convergence of the approximated solution sequence generated by the iterative method is investigated, showing that if the constrained matrix equation is consistent, the mixed solution group can be obtained after a finite number of iterations. Moreover, for a given matrix, its best approximation is obtained, which is the mixed solution of the matrix equation with sub-matrix constraints. Finally, a large number of numerical experiments are carried out, and results show that the algorithm is effective not only in image restoration, but also in the general case for both small-scale and large-scale matrices.

Keywords: Gradient-like projection method; Centro-symmetric matrix; Bisymmetric matrix; Mixed solution (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:411:y:2021:i:c:s009630032100549x

DOI: 10.1016/j.amc.2021.126460

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