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2011•Unpublished venueRequires access

Iterative solutions for general coupled matrix equations with real coefficients

Li Xie, Huizhong Yang, Yan‐Jun Liu, Feng Ding

Open publisher page 2 citations

Abstract

This paper applies the hierarchical identification principle and the gradient search method to study iterative solutions for a class of general coupled matrix equations with real coefficients. As long as the convergence factors are appropriately chosen, the proposed algorithms for any initial values can provide iterative solutions that are arbitrarily close to the unique solutions of the equations. Two numerical examples are given to demonstrate the effectiveness of the proposed algorithms.

About this research paper

What this paper is about

This paper applies the hierarchical identification principle and the gradient search method to study iterative solutions for a class of general coupled matrix equations with real coefficients. As long as the convergence factors are appropriately chosen, the proposed algorithms for any initial values can provide iterative solutions that are arbitrarily close to the unique solutions of the equations. Two numerical examples are given to demonstrate the effectiveness of the proposed algorithms.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Method / approach

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Available abstract

This paper applies the hierarchical identification principle and the gradient search method to study iterative solutions for a class of general coupled matrix equations with real coefficients. As long as the convergence factors are appropriately chosen, the proposed algorithms for any initial values can provide iterative solutions that are arbitrarily close to the unique solutions of the equations. Two numerical examples are given to demonstrate the effectiveness of the proposed algorithms.

Key concepts: Iterative method, Convergence (economics), Matrix (chemical analysis), Applied mathematics, Computer science, Matrix splitting, Local convergence, Matrix-free methods

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