Search results
Results from the WOW.Com Content Network
The convergence properties of the Gauss–Seidel method are dependent on the matrix . Namely, the procedure is known to converge if either: Namely, the procedure is known to converge if either: A {\displaystyle \mathbf {A} } is symmetric positive-definite , [ 6 ] or
Jacobi method; Gauss–Seidel method. Successive over-relaxation (SOR) — a technique to accelerate the Gauss–Seidel method Symmetric successive over-relaxation (SSOR) — variant of SOR for symmetric matrices; Backfitting algorithm — iterative procedure used to fit a generalized additive model, often equivalent to Gauss–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 .
If Scarborough criterion is not satisfied then Gauss–Seidel method iterative procedure is not guaranteed to converge a solution. This criterion is a sufficient condition, [3] not a necessary one. If this criterion is satisfied then it means equation will be converged by at least one iterative method. The Scarborough criterion is used as a ...
The Jacobi method is a simple relaxation method. 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 standard convergence condition (for any iterative method) is when the spectral radius of the iteration matrix is less than 1: ((+)) < A sufficient (but not necessary) condition for the method to converge is that the matrix A is strictly or irreducibly diagonally dominant. Strict row diagonal dominance means that for each row, the absolute ...
A general iterative method converges for every initial vector if T is convergent, and under certain conditions if T is semi-convergent. ... Gauss–Seidel method ...
The Jacobi and Gauss–Seidel methods for solving a linear system converge if the matrix is strictly (or irreducibly) diagonally dominant. Many matrices that arise in finite element methods are diagonally dominant.