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Mathematics of Computation

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On Fourier-Toeplitz methods for separable elliptic problems


Authors: D. Fischer, G. Golub, O. Hald, C. Leiva and O. Widlund
Journal: Math. Comp. 28 (1974), 349-368
MSC: Primary 65F05; Secondary 65N20
DOI: https://doi.org/10.1090/S0025-5718-1974-0415995-2
MathSciNet review: 0415995
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Abstract: 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.


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DOI: https://doi.org/10.1090/S0025-5718-1974-0415995-2
Article copyright: © Copyright 1974 American Mathematical Society