For solving a set of linear equations, we seek the solution to the problem:
After k iterations we obtain an approaximation to the solution as:
where is the residual after k iterations.
as the difference between the exact and approaximate solution.
we obtain :
the purpose of iterations is to drive this residual to zero.
Stationary Iterative Methods
Iterative methods that can be expressed in the simple form:
When neither B nor c depend upon the iteration count (k), the iterative method is called stationary iterative method. Some of the stationary iterative methods are:
- Jacobi method
- Gauss-Seidel method
- Successive Overrelaxation (SOR) method and
- Symmetric Successive Overrelaxation (SSOR) method