摘要
众多学者对二次矩阵方程AX^(2)+BX+C=0的求解及应用进行了研究。为探索其高效数值解法,本研究提出一种基于交替方向乘子法(ADMM)的求解框架,通过建立适当的优化模型将原问题转化为可通过交替迭代高效求解的子问题,并系统分析ADMM算法的收敛性,从理论上保证了迭代过程的稳定性与解的可行性。通过数值实验验证,在合理选取算法参数的前提下,所提出的ADMM求解策略能够有效求解该二次矩阵方程,且具备良好的计算效率与数值稳定性。
Recently,some scholars have conducted new researches on the solution and application of the quadratic matrix equation AX^(2)+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.
作者
阳晴
马昌凤
YANG Qing;MA Changfeng(School of Mathematics and Statistics,Fujian Normal University,Fuzhou,Fujian 350007,China)
出处
《井冈山大学学报(自然科学版)》
2026年第2期1-8,共8页
Journal of Jinggangshan University (Natural Science Edition)
基金
国家自然科学基金项目(12371378)
福建省自然科学基金项目(2024J01980)。
