An Always Convergent Minimization Technique for the Solution of Polynomial Equations
J. A. Grant, G.D. Hitchins · IMA Journal of Applied Mathematics · 1971
This paper gives a new, always convergent, very simple and practical algorithm for determining initial approximations to the roots of polynomial equations with real co-efficients. It uses a combination of Newton's method to solve a pair of simultaneous non-linear equations and a modification of “steepest descent” on the sums of the squares of the equations to give a first approximation to a root. A general polynomial solver using this technique is described and an extension to more general equations is indicated.