( setf *read-default-float-format* 'long-float ) ( defparameter +MAXIMUM-NUMBER-OF-ITERATIONS+ 100 "The number of iterations beyond which the algorithm should cease its operation, regardless of its current solution. Set the default floating-point format to "long-float" in order to ensure correct operation on a wider range of numbers. According to the successive over-relaxation algorithm, the following table is obtained, representing an exemplary iteration with approximations, which ideally, but not necessarily, finds the exact solution, (3, −2, 2, 1), in 38 steps.Ī simple implementation of the algorithm in Common Lisp is offered below. Given a square system of n linear equations with unknown x:Ī =, x =, b =. These aspects are discussed in the thesis of David M. However, these methods were designed for computation by human calculators, requiring some expertise to ensure convergence to the solution which made them inapplicable for programming on digital computers. An example is the method of Lewis Fry Richardson, and the methods developed by R. Over-relaxation methods had been used before the work of Young and Frankel. Frankel in 1950 for the purpose of automatically solving linear systems on digital computers.
It was devised simultaneously by David M. A similar method can be used for any slowly converging iterative process.
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.
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