ERROR ANALYSIS OF k-FOLD PSEUDO-HALLEY'S METHOD FINDING A SIMPLE ZERO

Abstract

Given a nonlinear function f : R → R that has a simple real zero α, a new numerical method to be called k-fold pseudoHalley's method is proposed and it's error analysis is under investigation to confirm the convergence behavior near α. Under the assumption that f is sufficiently smooth in a small neighborhood of α, the order of convergence is found to be at least k +3. In addition, the corresponding asymptotic error constant is explicitly expressed in terms of k, α and f as well as the derivatives of f . A zerofinding algorithm is written and has been successfully implemented for numerous examples with Mathematica.

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