On Fourier-Toeplitz methods for separable elliptic problems
D. Fischer, Gene Howard Golub, O. Hald, Carlos Leiva, Olof B. Widlund · Mathematics of Computation · 1974
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.