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Title of Journal: Numer Algor

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Abbravation: Numerical Algorithms

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Springer US

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DOI

10.1002/food.19870310410

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1572-9265

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A global convergent derivativefree method for sol

Authors: Sascha Wörz Heinz Bernhardt
Publish Date: 2016/12/10
Volume: 76, Issue: 1, Pages: 109-124
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Abstract

Finding all zeros of a system of m in mathbb N real nonlinear equations in n in mathbb N variables often arises in engineering problems Using Newtons’ iterative method is one way to solve the problem however the convergence order is at most two it depends on the starting point there must be as many equations as variables and the function F which defines the system of nonlinear equations Fx=0 must be at least continuously differentiable In other words finding all zeros under weaker conditions is in general an impossible task In this paper we present a global convergent derivativefree method that is capable to calculate all zeros using an appropriate Schauder base The component functions of F are only assumed to be Lipschitzcontinuous Therefore our method outperforms the classical counterparts

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