ON THE HIGH-ORDER CONVERGENCE OF THE k-FOLD PSEUDO-CAUCHY'S METHOD FOR A SIMPLE ROOT

Abstract

In this study the k-fold pseudo-Cauchy's method of order k + 3 is proposed from the classical Cauchy's method defined by f 00(xn) ·(cid:0)1−p1 − 2f (xn)f 00(xn)/f 0(xn)2 (cid:1). an iteration xn+1 = xn− f 0(xn) The convergence behavior of the asymptotic error constant is investigated near the corresponding simple zero. A root-finding algorithm with the k-fold pseudo-Cauchy's method is described and computational examples have successfully confirmed the current analysis.

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