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

The asymptotic convergence rates of many standard iterativemethods for the solution of linear equations can be shown todepend inversely on the P-condition number of the co-efficientmatrix. The notion of minimizing the P-condition number andhence maximizing the convergence rate by the introduction ofa new pre-conditioning factor is shown to be computationallyfeasible. The application of this idea to the method of SimultaneousDisplacement, Richardson's method and other iterative methods,are discussed and numerical examples given to illustrate itseffectiveness.