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Preconditioned GMRES method for a class of Toeplitz linear systems in fractional eigenvalue problems
Computational and Applied Mathematics ( IF 2.998 ) Pub Date : 2020-08-19 , DOI: 10.1007/s40314-020-01258-9
Qian Zuo , Ying He

In this paper, we consider the solution of a class of Toeplitz linear systems coming from the fractional eigenvalue problems. We construct the Strang circulant matrix as a preconditioner to solve the Toeplitz linear systems, and analyze the properties of eigenvalues of the preconditioned coefficient matrix. We also propose the preconditioned generalized minimal residuals method for solving this linear systems, and give the computational costs of this algorithm. The numerical examples show the effecticiency of our method.

中文翻译:

分数阶特征值问题中一类Toeplitz线性系统的预处理GMRES方法

在本文中,我们考虑一类来自分数阶特征值问题的Toeplitz线性系统的解。我们构造了Strang循环矩阵作为求解Toeplitz线性系统的前提,并分析了预处理系数矩阵的特征值的性质。我们还提出了求解该线性系统的预处理广义最小残差方法,并给出了该算法的计算成本。数值例子表明了我们方法的有效性。
更新日期:2020-08-19
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