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2009•Unpublished venueRequires access

Some Modified Newton-Type Methods with Order of Convergence Varied from Two to Six under Weak Conditions

Liang Fang, Guoping He, Yunhong Hu, Li Sun

Open publisher page 8 citations

Abstract

We present some modified Newton-type methods for solving nonlinear equations. These algorithms are free from second derivatives and permit f'(x) = 0 in some iteration points. The convergent analysis demonstrates that the order of convergence and the efficiency index of the present methods are better than that of the classical Newton's method. Some numerical examples are given to illustrate their efficiency and performance.

About this research paper

What this paper is about

We present some modified Newton-type methods for solving nonlinear equations. These algorithms are free from second derivatives and permit f'(x) = 0 in some iteration points. The convergent analysis demonstrates that the order of convergence and the efficiency index of the present methods are better than that of the classical Newton's method. Some numerical examples are given to illustrate their efficiency and performance.

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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We present some modified Newton-type methods for solving nonlinear equations. These algorithms are free from second derivatives and permit f'(x) = 0 in some iteration points. The convergent analysis demonstrates that the order of convergence and the efficiency index of the present methods are better than that of the classical Newton's method. Some numerical examples are given to illustrate their efficiency and performance.

Key concepts: Newton's method, Convergence (economics), Steffensen's method, Local convergence, Type (biology), Mathematics, Nonlinear system, Applied mathematics

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Some Modified Newton-Type Methods with Order of Convergence Varied from Two to Six under Weak Conditions — Research Paper | ScholarLens