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 
.
Symmetric Successive Overrelaxation Method
See also
Jacobi Method, Nonstationary Iterative Method, Stationary Iterative Method, Successive Overrelaxation MethodThis 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.Referenced on Wolfram|Alpha
Symmetric Successive Overrelaxation MethodCite 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