The optimal solution of the extrapolation problem of a first order scheme

Abstract

In this paper it is assumed that a first order stationary iterative scheme for the solution of a linear system of equations is given. It is also assumed that all the eigenvalues of the iteration matrix of the scheme are known and have real parts which are all either less or greater than one. Under the previous assumptions the solution of the optimization problem by means of an extrapolation scheme of the original one is studied, analyzed and found. Finally an algorithm for finding the optimum parameters is presented and a number of applications and examples is given.

Keywords:

• First order stationary iterative scheme
• linear system of equations
• iteration matrix
• extrapolation scheme

C.R. Categories::

• 5.14