AbstractsMathematics

This paper makes available practical algorithms and their associated FORTRAN IV computer programs for finding the roots of polynomial equations. The purpose of this paper is to examine effective algorithms for solving polynomial algebraic equations in one unknown on a digital computer. The advent of high - speed digital computing systems makes it practical to examine numerical methods which otherwise would be too time consuming if not impossible. Algorithms requiring only the polynomial coefficients are examined since they can be used as subprograms to solve polynomial equations which arise in other computer programs. The above considerations have lead to the examination of the following algorithms: Lehmeris algorithm, (used to find rough approximations to the roots). a) The Newton-Raphson algorithm, (used to refine the root approximations). (ii). Muller s algorithm. (iii). Rutishauser's Quotient-Difference (QD) algorithm, (used to find rough approximations to the roots). a) Newton-Raphson's algorithm, (used to refine approximations to simple roots). b) Bairstow's algorithm, (used to refine approximations to two roots i. e. complex conjugates). (iv). The Steepest Descent algorithm.