In numerical linear algebra, the Gauss-Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel, and can be applied to any matrix with non-zero diagonal elements, though convergence is only guaranteed when the matrix is strictly diagonally dominant, or symmetric and positive definite. The method was first mentioned only in a private letter from Gauss to his student Gerling in 1823, and was not published until 1874, by Seidel.
Facts
Classification
Design Technique Connections
In Field
Source Gauss-Seidel method (Wikipedia)
Uses Design Technique
Source Wolfram MathWorld: Gauss-Seidel Method
Sources
1. Wolfram MathWorld: Gauss-Seidel Method
Wolfram MathWorldMathWorld, article text (design technique)
Since each component of the new iterate depends upon all previously computed components, the updates cannot be done simultaneously as in the Jacobi method
Uses Design Technique: Iterative Refinement, MathWorld, article text (technique relation)
Since each component of the new iterate depends upon all previously computed components, the updates cannot be done simultaneously as in the Jacobi method
View the Source Gauss-Seidel method (Wikipedia)
In Field: Computational Science, Lead sentenceQuote, In Field: Computational Science, Lead sentence
Gauss-Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations.
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