Local convergence for composite Chebyshev-type methods

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Communications in Advanced Mathematical Sciences
Volume:1 Issue:1
Local convergence for composite Chebyshev-type methods

Local convergence for composite Chebyshev-type methods

Authors : İoannis K ARGYROS, Santhosh GEORGE

Pages : 84-90

Doi:10.33434/cams.441220

View : 19 | Download : 15

Publication Date : 2018-09-30

Article Type : Research Paper

Abstract :We replace Chebyshev`s method for solving equations requiring the second derivative by a Chebyshev-type second derivative free method. The local convergence analysis of the new method is provided using hypotheses only on the first derivative in contrast to the Chebyshev method using hypotheses on the second derivative. This way we extend the applicability of the method. Numerical examples are also used to test the convergence criteria and to obtain error bounds and also the radius of convergence.
Keywords : Chebyshev method, Newton method, Fr`echet derivative, Local convergence, Divided differences

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