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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 .
In numerical linear algebra, the method of successive over-relaxation (SOR) is a variant of the Gauss–Seidel method for solving a linear system of equations, resulting in faster convergence. A similar method can be used for any slowly converging iterative process.
When approximating the constraints locally to first order, this is the same as the Gauss–Seidel method. For small matrices it is known that LU decomposition is faster. Large systems can be divided into clusters (for example, each ragdoll = cluster). Inside clusters the LU method is used, between clusters the Gauss–Seidel method is used. The ...
The Gauss–Seidel method is an improvement upon the Jacobi method. Successive over-relaxation can be applied to either of the Jacobi and Gauss–Seidel methods to speed convergence. Multigrid methods
The Stein-Rosenberg theorem, proved in 1948, states that under certain premises, the Jacobi method and the Gauss-Seidel method are either both convergent, or both divergent. If they are convergent, then the Gauss-Seidel is asymptotically faster than the Jacobi method.
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On the other hand, approximated results of reaction force is due to the slow convergence of typical Projected Gauss Seidel solver resulting in abnormal bouncing. Any type of free-moving compound physics object can demonstrate this problem, but it is especially prone to affecting chain links under high tension, and wheeled objects with actively ...
Other notable examples include solving partial differential equations, [1] the Jacobi kernel, the Gauss–Seidel method, [2] image processing [1] and cellular automata. [3] The regular structure of the arrays sets stencil techniques apart from other modeling methods such as the Finite element method.