caa a22 4500 465751458 CHVBK 20180323111834.0 cr unu---uuuuu 170327e19900601xx s 000 0 eng 10.1007/BF02241866 doi (NATIONALLICENCE)springer-10.1007/BF02241866 Recurrence relations for rational cubic methods I: The Halley method [Elektronische Daten] [V. Candela, A. Marquina] Rekursions-Beziehungen für rationale kubische Verfahren I: Das Halley-Verfahren In this paper we present a system of a priori error bounds for the Halley method in Banach spaces. Our theorem supplies sufficient conditions on the initial point to ensure the convergence of Halley iterates, by means of a system of "recurrence relations”, analogous to those given for the Newton method by Kantorovich, improving previous results by Döring [4]. The error bounds presented are optimal for second degree polynomials. Other rational cubic methods, as the Chebyshev method, will be treated in a subsequent paper. Springer-Verlag, 1990 Third order iterative methods nationallicence a priori error bounds nationallicence non-linear equations nationallicence Candela V. Departmento de Análisis Matemático, University of Valencia, C/Dr. Moliner, 50, 46100, Burjassot (Valencia), Spain aut Marquina A. Departmento de Análisis Matemático, University of Valencia, C/Dr. Moliner, 50, 46100, Burjassot (Valencia), Spain aut Computing Springer-Verlag 44/2(1990-06-01), 169-184 0010-485X 44:2<169 1990 44 607 https://doi.org/10.1007/BF02241866 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02241866 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Candela V. Departmento de Análisis Matemático, University of Valencia, C/Dr. Moliner, 50, 46100, Burjassot (Valencia), Spain aut NATIONALLICENCE 700 1- Marquina A. Departmento de Análisis Matemático, University of Valencia, C/Dr. Moliner, 50, 46100, Burjassot (Valencia), Spain aut NATIONALLICENCE 773 0- Computing Springer-Verlag 44/2(1990-06-01), 169-184 0010-485X 44:2<169 1990 44 607 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 465751458 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer