Sparse Matrix Techniques Copenhagen 1976 Advanced Course Held at the

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572 Sparse Matrix Techniques Copenhagen 1976

Advanced Course Held at the Technical University of Denmark Copenhagen, August 9-12, 1976

Edited by V. A. Barker

Springer-Verlag Berlin-Heidelberg • New York 1977

Editor V. A. Barker Institute for Numerical Analysis Technical University of Denmark Copenhagen/Denmark

Library of Congress Cataloging in Publication Data

Course in Advanced Sparse Matrix Techniques, Technical University of Denmark, 1976. Sparse matrix teehuiqueSo (Lecture notes in mathematics ; 572) lo Matrices--Addresses, essays, lectures. 2. Equations, Simultaneous--Addresses, essays, lectures. Io Barker, Vincent Allan~ 1934II. Title~ III. Series: Lecture notes in m~thematics (Berlin) ; 572. QA3.L28 no. 572 [QA185] 510'.8s [512.9'43] 77-1128

AMS Subject Classifications (1970): 65-02, 65 F05, 65F 10, 65 F15, 65 F20, 65N20, 94A20 ISBN 3-540-08130-5 ISBN 0-38?-08130-5

Springer-Verlag Berlin • Heidelberg • New York Springer-Verlag New York • Heidelberg • Berlin

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 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. © by Springer-Verlag Berlin • Heidelberg 1977 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 43210

PREFACE

These notes were w r i t t e n f o r the "Course in Advanced Sparse Matrix Techniques" held at the Technical Univecsity of Denmark, Copenhagen, on August 9-12, 1976.

The

course was arranged by the I n s t i t u t e fo r Numerical Analysis, a department of the U n i v e r s i t y , with the f i n a n c i a l support of the Danish Natural Science Research Council.

There were 72 participants from 9 countries. The purpose of the course was to present scientists and engineers in higher

education and industry with s t a t e - o f - t h e - a r t material in one of the most r a p i d l y growing areas in numerical analysis.

I t was decided at the outset to concentrate on

a few topics of central importance rather than attempt to be comprehensive, and to i n v i t e as lecturers leading researchers in those topics.

The program was the f o l l o w -

ing: OWE AXELSSON, Chalmers University of Technology, Sweden; Solution of l i n e a r systems of equations: i t e r a t i v e methods. J. ALAN GEORGE, University of Waterloo, Canada; Solution of l i n e a r systems of equations: d i r e c t methods f or f i n i t e element problems. JOHN K. REID, Atomic Energy Research Establishment, Harwell, England; Solution of l i n e a r systems of equations: d i r e c t methods (general). AXEL RUHE, University of Ume~, Sweden; Computation of eigenvalues and eigenvectors. Four l-hour lectures were devoted to each topic. Most of the s t a f f of the I n s t