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2011•Unpublished venueRequires access

A Class of Fifth-Order Convergence Variants of Newton's Method and Its Acceleration

Jing Cai

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Abstract

Based on the classical Newton's method and the midpoint Newton's method,the paper presented a new fifth-order convergent iterative algorithm and its acceleration formula for nonlinear equations.Results of the numerical experiments show that the proposed algorithm is more accurate and efficient than the classical Newton's method and several existing Newton improving formats,such as Midpoint Newton's method,Geometrical mean Newton's method,Harmonic mean Newton's method and Simpson Newton's method.

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What this paper is about

Based on the classical Newton's method and the midpoint Newton's method,the paper presented a new fifth-order convergent iterative algorithm and its acceleration formula for nonlinear equations.Results of the numerical experiments show that the proposed algorithm is more accurate and efficient than the classical Newton's method and several existing Newton improving formats,such as Midpoint Newton's method,Geometrical mean Newton's method,Harmonic mean Newton's method and Simpson Newton's method.

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Available abstract

Based on the classical Newton's method and the midpoint Newton's method,the paper presented a new fifth-order convergent iterative algorithm and its acceleration formula for nonlinear equations.Results of the numerical experiments show that the proposed algorithm is more accurate and efficient than the classical Newton's method and several existing Newton improving formats,such as Midpoint Newton's method,Geometrical mean Newton's method,Harmonic mean Newton's method and Simpson Newton's method.

Key concepts: Steffensen's method, Newton's method, Acceleration, Newton's method in optimization, Mathematics, Convergence (economics), Local convergence, Midpoint

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