In this chapter we analyse Stationary iterative methods for solving systems
. A stationary iterative method can be derived from a splitting of the coefficient matrix as the difference of two matrices and generates a sequence of vectors that is expected to converge to the solution.
We iterate Mx^(k+1) = Nx^(k) +b, using the splitting A = M −N. Even though this is a relatively straightforward class of iterative methods.
Iterative methods that can be expressed in the simple form x^(k+1) = Bx^(k) +c
(where neither nor depend on the iteration count ). The oldest and simplest iterations for solving linear systems are stationary iterations. we will focus on 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.
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