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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 .
Relaxation methods are used to solve the linear equations resulting from a discretization of the differential equation, for example by finite differences. [ 2 ] [ 3 ] [ 4 ] Iterative relaxation of solutions is commonly dubbed smoothing because with certain equations, such as Laplace's equation , it resembles repeated application of a local ...
In some cases, Newton's method can be stabilized by using successive over-relaxation, or the speed of convergence can be increased by using the same method. In a robust implementation of Newton's method, it is common to place limits on the number of iterations, bound the solution to an interval known to contain the root, and combine the method ...
In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the i-th approximation (called an "iterate") is derived from the previous ones.
In applied mathematics, symmetric successive over-relaxation (SSOR), [1] is a preconditioner. If the original matrix can be split into diagonal, lower and upper triangular as = + + then the SSOR preconditioner matrix is defined as = (+) (+)
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 .
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; Modified Richardson iteration
See, in particular, the successive over-relaxation (SOR) and symmetric successive over-relaxation (SSOR) methods. [2] When David Young first began his research on iterative methods in the late 1940s, there was some skepticism with the idea of using iterative methods on the new computing machines to solve industrial-size problems. Ever since ...