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Zbl 1122.65338
Kou, Jisheng; Li, Yitian
An improvement of the Jarratt method. (English)
[J] Appl. Math. Comput. 189, No. 2, 1816-1821 (2007). ISSN 0096-3003

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.

MSC 2000:: *65H05 Single nonlinear equations (numerical methods)

Keywords: Jarratt method; Newton method; non-linear equations; root-finding; iterative method; convergence; numerical tests

Cited in: Zbl 1187.65052 Zbl 1184.65054 Zbl 1170.65032 Zbl 1154.65327

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