On Fourier-Toeplitz methods for separable elliptic problems
On Fourier-Toeplitz methods for separable elliptic problems
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DOI：
10.1090/s0025-5718-1974-0415995-2
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发表时间：
1974-05
影响因子：
2
通讯作者：
D. Fischer;G. Golub;O. Hald;C. Leiva;O. Widlund
中科院分区：
文献类型：
--
作者：
D. Fischer;G. Golub;O. Hald;C. Leiva;O. Widlund
近年来发展了一些求解分离变量的椭圆型微分方程的快速数值方法。本文提出了Fourier-Toeplitz方法，作为Hockney和Buneman方法的替代方法。它是基于快速傅里叶变换和Toeplitz分解。使用Toeplitz分解与Sherman-Morrison公式相结合，也系统地探索了Toeplitz带矩阵代数方程的线性系统，或几乎Toeplitz形式。最后给出了数值实验结果。
Some very fast numerical methods have been developed in recent years for the solution of elliptic differential equations which allow for separation of variables. In this paper, a Fourier-Toeplitz method is developed as an alternative to the well-known methods of Hockney and Buneman. It is based on the fast Fourier transform and Toeplitz factorizations. The use of Toeplitz factorizations combined with the Sherman-Morrison formula is also systematically explored for linear systems of algebraic equations with band matrices of Toeplitz, or almost Toeplitz form. Finally, results of numerical experiments are described.