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

Ashim Kumar and João R. Cardoso

Applied Mathematics and Computation, 2018, vol. 333, issue C, 246-253

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.

Keywords: Yang–Baxter-like matrix equation; Fréchet derivative; Iterative methods; Convergence; Stability; Idempotent matrix (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:333:y:2018:i:c:p:246-253

DOI: 10.1016/j.amc.2018.03.078

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