ScholarLens Back to search
2014•Value EngineeringRequires access

A Gradient Iterative Algorithm for Solving the Coupled Sylvester Matrix Equations

Zhang Lon

Open publisher page 0 citations

Abstract

This paper presents a gradient iterative algorithm for solving the generalized coupled matrix equations based on the hierarchical identification principle and extending of the iterative algorithm for the AX=b or AX+XB=C, and the convergence of this method is also given. 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. Giving numerical example demonstrates the effectiveness of the proposed algorithm.

About this research paper

What this paper is about

This paper presents a gradient iterative algorithm for solving the generalized coupled matrix equations based on the hierarchical identification principle and extending of the iterative algorithm for the AX=b or AX+XB=C, and the convergence of this method is also given. 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. Giving numerical example demonstrates the effectiveness of the proposed algorithm.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

This paper presents a gradient iterative algorithm for solving the generalized coupled matrix equations based on the hierarchical identification principle and extending of the iterative algorithm for the AX=b or AX+XB=C, and the convergence of this method is also given. 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. Giving numerical example demonstrates the effectiveness of the proposed algorithm.

Key concepts: Iterative method, Sylvester matrix, Mathematics, Sylvester equation, Matrix (chemical analysis), Convergence (economics), Matrix-free methods, Applied mathematics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
A Gradient Iterative Algorithm for Solving the Coupled Sylvester Matrix Equations — Research Paper | ScholarLens