Modified Dorn's algorithm with improved speed-up

Abstract

The polynomial evaluation is one of the most common standard problems and has attracted the attention of researches for many years. In this study a brief up-to-date survey of existing parallel methods is given and the possibility of improving the parallelisation of Dorn's algorithm [1] (which is the parallel implementation of the well known Horner's method) is studied. In a previous work [5] the decoupling algorithm [6] for solving bidiagonal systems has been simplified, modified and applied to parallelise Horner's method. This paper is the extension and the generalisation of the approach followed in [5] for Dorn's method by reformulating as a set of independent matrix equations with special bidiagonal coefficient matrices. These independent equations are solved in parallel leading to improvement in the speed-up of the algorithm. Performance parameters the speed-up and the efficiency expressions are given and a comparative analysis of the algorithm with the methods studied in [1] and [5] are presented in a table in terms of the total number of unit time steps, the number of processors used and the degree of polynomials.