Gauss-Seidel method
From CFD-Wiki
(Difference between revisions)
(fixed dot product notation) |
|||
Line 1: | Line 1: | ||
We seek the solution to set of linear equations: <br> | We seek the solution to set of linear equations: <br> | ||
- | :<math> A \ | + | :<math> A \cdot X = Q </math> <br> |
For the given matrix '''A''' and vectors '''X''' and '''Q'''. <br> | For the given matrix '''A''' and vectors '''X''' and '''Q'''. <br> |
Revision as of 20:33, 15 December 2005
We seek the solution to set of linear equations:
For the given matrix A and vectors X and Q.
In matrix terms, the definition of the Gauss-Seidel method can be expressed as :
Where D,L and U represent the diagonal, lower triangular and upper triangular matrices of coefficient matrix A and k is iteration counter.
The pseudocode for the Gauss-Seidel algorithm:
Algorithm
- Chose an intital guess to the solution
- for k := 1 step 1 untill convergence do
- for i := 1 step until n do
-
- for j := 1 step until i-1 do
- end (j-loop)
- for j := i+1 step until n do
- end (j-loop)
-
- end (i-loop)
- check if convergence is reached
- for i := 1 step until n do
- end (k-loop)
Return to Numerical Methods