NANAJun 6, 2011

A Technique to Composite a Modified Newton's Method for Solving Nonlinear Equations

arXiv:1106.09965 citationsh-index: 3
Originality Synthesis-oriented
AI Analysis

For researchers in numerical analysis, this offers an incremental improvement to root-finding methods by enhancing efficiency indices.

The paper presents a technique to improve the efficiency of solving nonlinear equations by composing iterative methods with a modified Newton's method, achieving higher convergence orders with minimal extra function evaluations.

A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to compose a given iterative method with a modified Newton's method that introduces just one evaluation of the function. To carry out this procedure some classical methods with different orders of convergence are used to obtain root-finders with higher efficiency index.

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