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2013•Journal of Anqing Teachers CollegeRequires access

A Gradient Iterative Algorithm for Solving the Coupled Matrix Equations

Hongcai Yin

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Abstract

This paper presents a gradient iterative algorithm for solving the coupled matrix equations AX+XB=C,DX+XTE=F by using the hierarchical identification principle and extending of the iterative algorithm for the matrix equation AX=b.The analysis shows that if the matrix equation has an unique solution,then the iterative solutions converge fast to the exact one for any initial value.A numerical example demonstrates the effectiveness of the proposed algorithm.

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What this paper is about

This paper presents a gradient iterative algorithm for solving the coupled matrix equations AX+XB=C,DX+XTE=F by using the hierarchical identification principle and extending of the iterative algorithm for the matrix equation AX=b.The analysis shows that if the matrix equation has an unique solution,then the iterative solutions converge fast to the exact one for any initial value.A numerical example demonstrates the effectiveness of the proposed algorithm.

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Available abstract

This paper presents a gradient iterative algorithm for solving the coupled matrix equations AX+XB=C,DX+XTE=F by using the hierarchical identification principle and extending of the iterative algorithm for the matrix equation AX=b.The analysis shows that if the matrix equation has an unique solution,then the iterative solutions converge fast to the exact one for any initial value.A numerical example demonstrates the effectiveness of the proposed algorithm.

Key concepts: Iterative method, Matrix splitting, Matrix-free methods, Matrix (chemical analysis), Mathematics, Convergent matrix, Applied mathematics, Algorithm

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