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Zbl 1122.65329
Chun, Changbum
Some improvements of Jarratt's method with sixth-order convergence. (English)
[J] Appl. Math. Comput. 190, No. 2, 1432-1437 (2007). ISSN 0096-3003

Summary: We present a one-parameter family of variants of Jarratt's fourth-order method for solving nonlinear equations. It is shown that the order of convergence of each family member is improved from four to six even though it adds one evaluation of the function at the point iterated by Jarratt's method per iteration. Several numerical examples are given to illustrate the performance of the presented methods.
MSC 2000:
*65H05 Single nonlinear equations (numerical methods)

Keywords: Newton's method; iterative methods; nonlinear equations; order of convergence; Jarratt's fourth-order method; numerical examples

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