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Kou, Jisheng; Li, Yitian

An improvement of the Jarratt method. (English) Zbl 1122.65338

Appl. Math. Comput. 189, No. 2, 1816-1821 (2007).
Summary: We present a variant of Jarratt method for solving non-linear equations. Per iteration the new method adds the evaluation of the function at another point in the procedure iterated by Jarratt method. As a consequence, the local order of convergence is improved from four for Jarratt method to six for the new method. The new multistep iteration scheme, based on the new method, is developed and numerical tests verifying the theory are also given.

Cited in 4 Reviews
Cited in 35 Documents

MSC:

65H05 Numerical computation of solutions to single equations

Keywords:

Jarratt method; Newton method; non-linear equations; root-finding; iterative method; convergence; numerical tests
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\textit{J. Kou} and \textit{Y. Li}, Appl. Math. Comput. 189, No. 2, 1816--1821 (2007; Zbl 1122.65338)
Full Text: DOI

References:

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