Fourier Analysis of the SOR Iteration
نویسندگان
چکیده
The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor co. We show that, for the standard model problem of Poisson's equation on a rectangle, the optimal co 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.
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I . Icase Fourier Analysis of the Sor Iteration
The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor w. We show that for the standard model problem of Poisson’s equation on a rectangle, the optimal w and corresponding convergence rate can be rigorously obtained by Fourier analysis. The trick is to tilt the space-time grid so that the SOR stencil becomes symmetrical. The tilted grid also gives insigh...
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