Lecture Notes in Mathematics Edited by A Dold and BEckmann 584 C. Brezinski Acceleration de la Convergence en Analyse Numerique Springer-Verlag Berlin. Heidelberg. New York 1977  Author Claude Brezinski UER d'iEEA-informatique Universite de Lille I B.P.36 59650 Villeneuve d'Ascq/France Library or Congress Cataloging in Publication Data Brezinski, Claude, 1941- Acceleration de la convergence en analyse numer- 1que. (Lecture notes in mathematics ; 584) Includes index. 1. Numerical analysis--Acceleration of conver- gence. 2. Series. 3. Fractions, Continued. I. I. Title. II. Series: Lecture notes in mathema- tics (Berlin) . 584. QA3.L28 no. 584 [QA297] 510'.8s [519.4] 77-6813 AMS Subject Classifications (1970): 65B05, 65B10, 65B15, 65B99, 65D15, 65F05, 65FlO, 65F15, 65HlO, 65L10 ISBN 3-540-08241-7 Springer-Verlag Berlin' Heidelberg' New Yark ISBN 0-387-08241-7 Springer-Verlag New York' Heidelberg' Berlin This w.ork is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, re- printing, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under 9 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. CO by Springer-Verlag Berlin' Heidelberg 1977 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210  Introduction Chapi tre I : I-I 1-2 1-3 1-4 1-5 1-6 Chapi tre II : II-I II-2 II-3 II-4 Chapitre III : III-I 1II-2 1II-3 1II-4 III-5 III-6 1II-7 Chapitre IV : PLAN COMPARAISON DE SUITES CONVERGENTES Rappels Ordre d'une suite Comparaison de deux suites Theoremes sur la comparaison L'indice de comparaison Developpemnt asymptotique d'une serie LES