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On a higher order secant method. (English) Zbl 1035.65057
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.

##### MSC:
 65J15 Equations with nonlinear operators (numerical methods) 47J25 Iterative procedures (nonlinear operator equations)
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##### References:
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