A Root Finding Algorithm for Parallel Architecture Machines

In this thesis a parallel algorithm for determining the zeros of any given analytic function is described. Parallelism is achieved by modifying the traditional bisection algorithm for architecture machines. Given any user supplied function f(X), continuous on the interval Ao ≤ x ≤ B0, and the tolerance of accuracy an algorithm of determining up to ten roots, with error of approximation less than or equal to tolerance, on parallel systems like Distributed Array Processor (OAP) and N-cube is considered. A variation of the bisection method has been adapted for this purpose. At each level of iteration a single new approximation to the root in question is found. At any stage results achieved should be considerably more accurate than the results achieved by the use of any iterative method on a serial machine because of localization of the approximation. This has been made possible by the use of much smaller intervals than the interval used for bisection algorithms, in determining the root. A performance comparison of speed of the approximation process using an algorithm on the DAP and and the N-cube is presented