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Iterative methods for finding commuting solutions of the Yang–Baxter-like matrix equation

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  • Kumar, Ashim
  • Cardoso, João R.

Abstract

The main goal of this paper is the numerical computation of solutions of the so-called Yang–Baxter-like matrix equation AXA=XAX, where A is a given complex square matrix. Two novel matrix iterations are proposed, both having second-order convergence. A sign modification in one of the iterations gives rise to a third matrix iteration. Strategies for finding starting approximations are discussed as well as a technique for estimating the relative error. One of the methods involves a very small cost per iteration and is shown to be stable. Numerical experiments are carried out to illustrate the effectiveness of the new methods.

Suggested Citation

  • Kumar, Ashim & Cardoso, João R., 2018. "Iterative methods for finding commuting solutions of the Yang–Baxter-like matrix equation," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 246-253.
    • Handle: RePEc:eee:apmaco:v:333:y:2018:i:c:p:246-253
    DOI: 10.1016/j.amc.2018.03.078
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    Cited by:

    1. Ashim Kumar & Dijana Mosić & Predrag S. Stanimirović & Gurjinder Singh & Lev A. Kazakovtsev, 2022. "Commuting Outer Inverse-Based Solutions to the Yang–Baxter-like Matrix Equation," Mathematics, MDPI, vol. 10(15), pages 1-16, August.
    2. Shanshan Hu & Yongxin Yuan, 2023. "Common Solutions to the Matrix Equations $$AX=B$$ A X = B and $$XC=D$$ X C = D on a Subspace," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 372-386, July.

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