井冈山大学学报（自然科学版）2026，Vol.47Issue(2)：1-8,8.DOI:10.3969/j.issn.1674-8085.2026.02.001
求解一类二次矩阵方程的ADMM方法
An ADMM method for solving a class of quadratic matrix equations
摘要
Abstract
Recently,some scholars have conducted new researches on the solution and application of the quadratic matrix equation AX2+BX+C=0.To explore its efficient numerical solution,this paper proposes a solution framework based on the alternating direction method of multipliers(ADMM).This method transforms the original problem into sub-problems that can be efficiently solved through alternating iterations by establishing an appropriate optimization model.The paper systematically analyzes the convergence of this ADMM algorithm,theoretically ensuring the stability of the iterative process and the feasibility of the solution.Further numerical experiments verify that,under the premise of reasonably selecting algorithm parameters,the proposed ADMM solution strategy can effectively solve this quadratic matrix equation and has good computational efficiency and numerical stability.关键词
ADMM算法/Sylvester方程/二次矩阵方程/数值实验Key words
ADMM algorithm/Sylvester equation/quadratic matrix equation/numerical experiment分类
数理科学引用本文复制引用
阳晴,马昌凤..求解一类二次矩阵方程的ADMM方法[J].井冈山大学学报（自然科学版）,2026,47(2):1-8,8.基金项目
国家自然科学基金项目(12371378) （12371378）
福建省自然科学基金项目(2024J01980) （2024J01980）
