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Zbl 1023.65051
Gutiérrez, J.M.; Hernández, M.A.
An acceleration of Newton's method: Super-Halley method. (English)
[J] Appl. Math. Comput. 117, No.2-3, 223-239 (2001). ISSN 0096-3003

Summary: From a study of the convexity we give an acceleration for Newton's method and obtain a new third order method. Then we use this method for solving nonlinear equations in Banach spaces, establishing conditions on convergence, existence and uniqueness of solution, as well as error estimates.

MSC 2000:: *65J15 Equations with nonlinear operators (numerical methods)
47J25 Methods for solving nonlinear operator equations (general)
65H05 Single nonlinear equations (numerical methods)

Keywords: convergence acceleration; nonlinear operator equation; super-Halley method; Newton's method; third order method; Banach spaces; convergence; error estimates

Cited in: Zbl 1206.65154

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Zentralblatt MATH Berlin [Germany]