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2011•Shandong Nongye Daxue xuebaoRequires access

A CLASS OF NEWTON-TYPE METHODS WITH THIRD-ORDER CONVERGENCE

Jiefang Wu

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Abstract

Using the first derivative at the midpoint,we present a new modified Newton′s method with third-order convergence,which has better convergence efficiency in some cases than the previous midpoint Newton's method .Numerical examples show that the presented method can compete with Newton′s method and other known third-order modifications of Newton′s method.Based on this new method,we obtain a family of Newton-type methods,which also converge cubically.

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What this paper is about

Using the first derivative at the midpoint,we present a new modified Newton′s method with third-order convergence,which has better convergence efficiency in some cases than the previous midpoint Newton's method .Numerical examples show that the presented method can compete with Newton′s method and other known third-order modifications of Newton′s method.Based on this new method,we obtain a family of Newton-type methods,which also converge cubically.

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Available abstract

Using the first derivative at the midpoint,we present a new modified Newton′s method with third-order convergence,which has better convergence efficiency in some cases than the previous midpoint Newton's method .Numerical examples show that the presented method can compete with Newton′s method and other known third-order modifications of Newton′s method.Based on this new method,we obtain a family of Newton-type methods,which also converge cubically.

Key concepts: Midpoint, Newton's method, Steffensen's method, Convergence (economics), Local convergence, Mathematics, Type (biology), Class (philosophy)

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