An Adaptive Method for Simultaneous Extraction of All Roots of Algebraic Polynomial

An adaptive algorithm of multi-point iterative method for simultaneous determination of all roots of polynomial equation is obtained. Its convergence rule was presented and proved. The computation is carried out by simple steepest descent rule with adaptive variable step-size. The specific examples illustrated that the proposed method can find simultaneously the roots of polynomials at a very rapid convergence and very high accuracy with less computation.