| Gauss-Seidel Method | |
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The Gauss-Seidel method (called Seidel's method by Jeffreys and Jeffreys 1988, p. 305) is a technique for solving the 
equations of the linear system of equations 
one at a time in sequence, and uses previously computed results as soon as they are available,
equations of the linear system of equations one at a time in sequence, and uses previously computed results as soon as they are available, 
There are two important characteristics of the Gauss-Seidel method should be noted. Firstly, the computations appear to be serial. Since each component of the new iterate depends upon all previously computed components, the updates cannot be done simultaneously as in the Jacobi method. Secondly, the new iterate 
depends upon the order in which the equations are examined. If this ordering is changed, the components of the new iterates (and not just their order) will also change.
depends upon the order in which the equations are examined. If this ordering is changed, the components of the new iterates (and not just their order) will also change. In terms of matrices, the definition of the Gauss-Seidel method can be expressed as
 |
where the matrices 
, 
, and 
represent the diagonal, strictly lower triangular, and strictly upper triangular parts of 
, respectively.
, , and represent the diagonal, strictly lower triangular, and strictly upper triangular parts of , respectively. The Gauss-Seidel method is applicable to strictly diagonally dominant, or symmetric positive definite matrices 
.
. 
Fuente :http://mathworld.wolfram.com/Gauss-SeidelMethod.html
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