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Multipoint Super-Halley Type Approximation Algorithms in Banach Spaces |
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| Authors: | J. A. Ezquerro M. A. Hernández |
| Affiliation: | Department of Mathematics and Computation , University of La Rioja , C/Luis de Ulloa s/n, Logro?o , 26004 , Spain E-mail: jezquer@dmc.unirioja.es, mahernan@dmc.unirioja.es |
| Abstract: | We use a new multipoint iteration of at least R-order three to solve a nonlinear operator equation in a Banach space. Under standard Newton-Kantorovich assumptions, we establish two Kantorovich convergence theorems using a new system of recurrence relations. We also give some explicit error bounds for this iteration. |
| Keywords: | Nonlinear equations in Banach spaces multipoint iterations third-order methods convergence theorem recurrence relations a priori error bounds 65J15 Classification A.M.S. 1991 The research reported herein was sponsored in part by the University of La Rioja (API-00/B16) and DGES (PB98-0198). |