Fourier Analysis of the SOR Iteration
- 1 July 1988
- journal article
- research article
- Published by Oxford University Press (OUP) in IMA Journal of Numerical Analysis
- Vol. 8 (3) , 273-279
- https://doi.org/10.1093/imanum/8.3.273
Abstract
The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor ω. We show that, for the standard model problem of Poisson's equation on a rectangle, the optimal ω and corresponding convergence rate can be obtained rigorously by Fourier analysis. The trick is to tilt the space-time grid so that the SOR stencil becomes symmetrical. The tilted grid also gives new insight into the relationships between the Gauss-Seidel and Jacobi iterations and between the lexicographic and red-black orderings, and into the modified equation analysis of Garabedian.Keywords
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