Parallel numerical methods for the solution of equations

Classical iterative procedures for the numerical solution of equations provide at each stage a single new approximation to the root in question. A technique is given for the development of numerical procedures which provide, at each stage, several approximations to a solution of an equation. The several approximations obtained in any iteration are computationally independent, making the methods of interest in a parallel processing environment. Convergence is insured by extracting the "best information" at each iteration. Several families of numerical procedures which use the technique are given. Statistics for the evaluation of the performance of the procedures in a parallel processing environment are developed and measurements of these statistics are reporte& These measurements are interpreted in a parallel processing environment. In such an environment the procedures obtained are superior to standard algorithms.