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

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  • Qu, Hongli
  • Xie, Dongxiu
  • Xu, Jie

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.

Suggested Citation

  • Qu, Hongli & Xie, Dongxiu & Xu, Jie, 2021. "A numerical method on the mixed solution of matrix equation ∑i=1tAiXiBi=E with sub-matrix constraints and its application," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    • Handle: RePEc:eee:apmaco:v:411:y:2021:i:c:s009630032100549x
    DOI: 10.1016/j.amc.2021.126460
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    References listed on IDEAS

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    1. Masoud Hajarian, 2016. "Least Squares Solution of the Linear Operator Equation," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 205-219, July.
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