The Use of Pre-conditioning in Iterative Methods for Solving Linear Equations with Symmetric Positive Definite Matrices

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Abstract
The asymptotic convergence rates of many standard iterative methods for the solution of linear equations can be shown to depend inversely on the P-condition number of the co-efficient matrix. The notion of minimizing the P-condition number and hence maximizing the convergence rate by the introduction of a new pre-conditioning factor is shown to be computationally feasible. The application of this idea to the method of Simultaneous Displacement, Richardson's method and other iterative methods, are discussed and numerical examples given to illustrate its effectiveness.

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