Symmetric Successive Overrelaxation Method

The symmetric successive overrelaxation (SSOR) method combines two successive overrelaxation method (SOR) sweeps together in such a way that the resulting iteration matrix is similar to a symmetric matrix it the case that the coefficient matrix A of the linear system Ax=b is symmetric. The SSOR is a forward SOR sweep followed by a backward SOR sweep in which the unknowns are updated in the reverse order. The similarity of the SSOR iteration matrix to a symmetric matrix permits the application of SSOR as a preconditioner for other iterative schemes for symmetric matrices. This is the primary motivation for SSOR, since the convergence rate is usually slower than the convergence rate for SOR with optimal omega.

See also

Jacobi Method, Nonstationary Iterative Method, Stationary Iterative Method, Successive Overrelaxation Method

This entry contributed by Noel Black and Shirley Moore, adapted from Barrett et al. (1994) (author's link)

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Barrett, R.; Berry, M.; Chan, T. F.; Demmel, J.; Donato, J.; Dongarra, J.; Eijkhout, V.; Pozo, R.; Romine, C.; and van der Vorst, H. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd ed. Philadelphia, PA: SIAM, 1994., L. and Young, D. Applied Iterative Methods. New York: Academic Press, 1981.Varga, R. Matrix Iterative Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1962.Young, D. Iterative Solutions of Large Linear Systems. New York: Academic Press, 1971.

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Symmetric Successive Overrelaxation Method

Cite this as:

Black, Noel and Moore, Shirley. "Symmetric Successive Overrelaxation Method." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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