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一类Toeplitz线性代数方程组的预处理GMRES方法

何颖, 刘皞   

  1. 南京航空航天大学数学系, 飞行器数学建模与高性能计算工业和信息化部重点实验室(南京航空航天大学), 南京 211106
  • 收稿日期:2019-07-17 发布日期:2021-05-13
  • 通讯作者: 刘皞,hliu@nuaa.edu.cn.
  • 基金资助:
    国家自然科学基金(11401305,11571171)和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.

何颖, 刘皞. 一类Toeplitz线性代数方程组的预处理GMRES方法[J]. 计算数学, 2021, 43(2): 177-191.

He Ying, Liu Hao. PRECONDITIONED GMRES METHOD FOR A CLASS OF TOEPLITZ LINEAR SYSTEMS[J]. Mathematica Numerica Sinica, 2021, 43(2): 177-191.

PRECONDITIONED GMRES METHOD FOR A CLASS OF TOEPLITZ LINEAR SYSTEMS

He Ying, Liu Hao   

  1. 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
  • Received:2019-07-17 Published:2021-05-13
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.

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