Recurrence Relations for Chebyshev - Type Methods ∗
نویسندگان
چکیده
The convergence of new second-order iterative methods are analyzed in Banach spaces by introducing a system of recurrence relations. A system of a priori error bounds for that method is also provided. The methods are defined by using a constant bilinear operator A, instead of the second Fréchet derivative appearing in the defining formula of the Chebyshev method. Numerical evidence that the methods introduced here accelerate the classical Newton iteration for a suitable A is provided.
منابع مشابه
On the semilocal convergence of efficient Chebyshev-Secant-type methods
We introduce a three-step Chebyshev–Secant-type method (CSTM) with high efficiency index for solving nonlinear equations in a Banach space setting. We provide a semilocal convergence analysis for (CSTM)using recurrence relations. Numerical examples validating our theoretical results are also provided in this study. © 2011 Elsevier B.V. All rights reserved.
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