Abstract
This chapter discusses the symmetric successive overrelaxation (SSOR) method and related methods. SSOR method can be considered as two half iterations. The first half iteration is the same as the SOR method, while the second half iteration is the SOR method with the equations taken in reverse order. The chapter discusses convergence properties of the SSOR method under the assumption that A is real and symmetric with positive diagonal elements. Convergence holds if and only if A is positive definite and 0<ω<2. The chapter also discusses the choice of ω when A is positive definite. A unique optimum value of ω exists, and in certain cases, a value of ω can be determined which, though not optimum, is sufficiently good so that when semi-iteration is used, the resulting method is better than the SOR method by an order-of-magnitude. The chapter also describes the methods related to the SSOR method, including the unsymmetric SOR method and unsymmetric modified SOR methods.
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