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# 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 of the linear system 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 .

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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## References

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. http://www.netlib.org/linalg/html_templates/Templates.html.Hageman, 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. https://mathworld.wolfram.com/SymmetricSuccessiveOverrelaxationMethod.html