Modified Richardson iteration
Iterative method used to solve a linear system of equations / From Wikipedia, the free encyclopedia
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Modified Richardson iteration is an iterative method for solving a system of linear equations. Richardson iteration was proposed by Lewis Fry Richardson in his work dated 1910. It is similar to the Jacobi and Gauss–Seidel method.
We seek the solution to a set of linear equations, expressed in matrix terms as
The Richardson iteration is
where is a scalar parameter that has to be chosen such that the sequence converges.
It is easy to see that the method has the correct fixed points, because if it converges, then and has to approximate a solution of .