摘要
本文研究一类来源于分数阶特征值问题的Toeplitz线性代数方程组的求解.构造Strang循环矩阵作为预处理矩阵来求解该Toeplitz线性代数方程组,分析了预处理后系数矩阵的特征值性质.提出求解该线性代数方程组的预处理广义极小残量法(PGMRES),并给出该算法的计算量.数值算例表明了该方法的有效性.
In this paper,we consider the solution of a class of Toeplitz linear systems derived from the fractional eigenvalue problems.We construct the Strang circulant matrix as a preconditioner to solve this Toeplitz linear systems,and analyze the properties of eigenvalues of the preconditioned coefficient matrix.We also propose the preconditioned generalized minimal residuals method(PGMRES)for solving this linear systems,and give the computational costs of this algorithm.The numerical examples show the effecticiency of our method.
作者
何颖
刘皞
He Ying;Liu Hao(Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA),MIIT,Nanjing 211106,China)
出处
《计算数学》
CSCD
北大核心
2021年第2期177-191,共15页
Mathematica Numerica Sinica
基金
国家自然科学基金(11401305,11571171)
南京航空航天大学研究生创新基地(实验室)开放基金(kfjj20180801)资助.
