Iterative methods
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| - | When neither '''B''' nor '''c''' depend upon the iteration count (k), the iterative method is called stationary iterative method. | + | 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: <br> |
| + | #Jacobi method | ||
| + | #Gauss-Seidel method | ||
| + | #Successive Overrelaxation (SOR) method and | ||
| + | #Symmetric Successive Overrelaxation (SSOR) method | ||
Revision as of 22:33, 17 September 2005
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.
Defining:
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
