Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation

Jia, Zhigang; Zhao, Mi; Wang, Minghui; Ling, Sitao

doi:10.1155/2014/681605

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Cited by 7 publications

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“…stuidied by [3][4][5][6] and the more related matrix equations like X n = M XM * and X n = A + M X −1 M * treated in [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

An iterative method to solve the nonlinear matrix equation $X^p =A+\sum\limits_{i = 1}^m {M_i^*(B+X^{-1})^{-1}{M_i}} $

Peng

et al. 2022

Preprint

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Note: Please see pdf for full title and abstract with equations. Nonlinear matrix equations $X^p =A+\sum\limits_{i = 1}^m {M_i^*(B+X^{-1})^{-1}{M_i}} $ has extensive applications in control theory, ladder networks, dynamic programming and stochastic filtering. In this paper a fixed point acceleration iteration algorithm is proposed and, based on the basic characteristics of the Thompson distance, the convergence and error estimator of the proposed algorithm are proved. Numerical comparison experiments show that the proposed algorithm is feasible and effective. Mathematics Subject Classification (2010): 15A24 , 65F30.

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“…stuidied by [3][4][5][6] and the more related matrix equations like X n = M XM * and X n = A + M X −1 M * treated in [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%