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Stationary Iterative Methods

Iterative methods that can be expressed in the simple form

(where neither nor depend upon the iteration count ) are called stationary iterative methods. In this section, we present the four main stationary iterative methods: the Jacobi method, the Gauss-Seidel method, the Successive Overrelaxation (SOR) method and the Symmetric Successive Overrelaxation (SSOR) method. In each case, we summarize their convergence behavior and their effectiveness, and discuss how and when they should be used. Finally, in §, we give some historical background and further notes and references.

• The Jacobi Method
  • Convergence of the Jacobi method
• The Gauss-Seidel Method
• The Successive Overrelaxation Method
  • Choosing the Value of Omega
• The Symmetric Successive Overrelaxation Method
• Notes and References