井冈山大学学报（自然科学版）2025，Vol.46Issue(4)：1-9,9.DOI:10.3969/j.issn.1674-8085.2025.04.001
求解Sylvester矩阵方程的加速多步Smith-内外迭代算法
ACCELERATED MULTI-STEP SMITH-INNER-OUTER ITERATION ALGORITHM FOR SOLVING SYLVESTER MATRIX EQUATION
摘要
Abstract
In this paper,we introduce a new accelerated multi-step Smith-inner-outer iteration algorithm for solving Sylvester matrix equation.This approach involves the careful selection of special initial matrices and applies the convergence behavior of series to enhance the algorithm's performance.Compared to the traditional multi-step Smith-inner-outer iteration algorithm,our proposed method demonstrates superior convergence properties.Meanwhile,the article provides some suggestions for the selection of parameters in the proposed algorithm.Finally,two numerical examples are used to verify the superiority of the proposed algorithm for solving the Sylvester matrix equation compared to the inner-outer iteration method,multi-step Smith-inner-outer iteration algorithm,relaxed multi-step Smith-inner-outer iteration algorithm,and shifted multi-step Smith-inner-outer iteration algorithm.关键词
内外迭代法/加速多步Smith-内外迭代算法/Sylvester矩阵方程Key words
inner-outer iterative method/accelerated multi-step Smith-inner-outer iteration method/sylvester matrix equation分类
数理科学引用本文复制引用
罗兰,唐嘉..求解Sylvester矩阵方程的加速多步Smith-内外迭代算法[J].井冈山大学学报（自然科学版）,2025,46(4):1-9,9.基金项目
国家自然科学基金项目(12371378) （12371378）
