Gauss Sediel

Gauss Seidel

The Gauss-Seidel method is a technique for solving the equations of the linear system of equations Ax=b 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.
In terms of matrices, the definition of the Gauss-Seidel method can be expressed as

where the matrices D,-L , and -U represent the diagonal, strictly lower triangular, and strictly upper triangular parts of A, respectively.
The Gauss-Seidel method is applicable to strictly diagonally dominant, or symmetric positive definite matrices A.

Example:
gauss-sediel

Gauss seidel with relaxation

Example:

Métodos iterativos, gauss seidel con relajación

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Bibliography:

• Hageman, L. and Young, D. Applied Iterative Methods. New York: Academic Press, 1981.

• http://mathworld.wolfram.com/Gauss-SeidelMethod.html

• http://matematicas.unal.edu.co/hmora/mnq.pdf

• http://www.slideshare.net/freysan/mtodos-iterativos-gauss-seidel-con-relajacin