Recurrence Relations for Chebyshev-Type Methods |
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| Authors: | J A Ezquerro M A Hernández |
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| Institution: | (1) Department of Mathematics and Computation, University of La Rioja, C/ Luis de Ulloa s/n, 26004 Logrono, Spain, jezquer@dmc.unirioja.es, mahernan@dmc.unirioja.es, ES |
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| Abstract: | 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.
Accepted 23 October 1998 |
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| Keywords: | , Nonlinear equations in Banach spaces, Second-order methods, Newton's method, A priori error bounds, AMS Classification,,,,,,47H17, 65J15, |
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