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Zbl 1035.65057
Amat, Sergio; Busquier, Sonia
On a higher order secant method. (English)
[J] Appl. Math. Comput. 141, No. 2-3, 321-329 (2003). ISSN 0096-3003

A modified secant method is introduced for solving a nonlinear equation $f(x)=0$. The secant of $f(x)$ at $x_{k}$ is replaced by a higher order approximation. It is show that this method can have quadratic convergence as the Newton method. Global monotonic convergence is proven for real functions. In Banach space, the convergence is established with relaxed Kantorovich-Ostrowski type conditions. Numerical examples confirm the conclusions.
[Zhen Mei (Toronto)]

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

Keywords: secant method; Newton method; nonlinear operator equation; quadratic convergence; monotonic convergence; Banach space; numerical examples

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