Handbook for Automatic Computation Volume II: Linear Algebra
The development of the internationally standardized language ALGOL has made it possible to prepare procedures which can be used without modification whenever a computer with an ALGOL translator is available. Volume Ia in this series gave details of the re
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Herausgegeben von
J. L. Doob
. A. Grothendieck . E. Heinz . F. Hirzebruch E. Hopf . H. Hopf . W. Maak . S. MacLane . W. Magnus J. K. Moser . M. M. Postnikov . F. K. Schmidt . D. S. Scott K. Stein
Geschäftsführende Herausgeber B. Eckmann und B. L. van der Waerden
Handbook for Automatie Computation Edited by
F. L. Bauer· A. S. Householder . F. W. J. Olver K. Samelson . E. Stiefel H. Rutishauser
t.
Volume II
J. H.Wilkinson . C. Reinsch
Linear Algebra Chief editor F. L. Bauer
Springer-Verlag Berlin Heidelberg NewYork 1971
Dr.
J. H. Wilkinson, F.R.S.
National Physical Laboratory, Teddington. Middlesex:
Dr. C. Reinsch Mathematisches Institut der Technischen Universitiit 8 Munchen 2, Arcisstr. 21
Geschaftsfiihrende Herausgeber:
Prof. Dr. B. Eckmann Eidgenossische Technische Hochschule Zurich
Prof. Dr. B. L. van der Waerden Mathematisches Institut der Universitat Zurich
AMS Subject Classifications (1971) Primary 65 Fxx, 15-04 Secondary 65 G OS, 90C 05
ISBN 978-3-642-86942-6 ISBN 978-3-642-86940-2 (eBook) 001 10.1007/978-3-642-86940-2
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@ by Springer-Verlag Berlin' Heidelberg 1971 • Library of Congress Softcover reprint of the hardcover 1st edition 1971
Catalog Card Number 70-163 742 .
Preface The development of the internationally standardized language ALGOL has made it possible to prepare procedures which can be used without modification whenever a computer with an ALGOL translator is available. Volume Ia in this series gave details of the restricted version of ALGOL which is to be employed throughout the Handbook, and volume Ib described its implementation on a computer. Each of the subsequent volumes will be devoted to a presentation of the basic algorithms in some specific areas of numerical analysis. This is the first such volume and it was feIt that the topic Linear Algebra was a natural choice, since the relevant algorithms are perhaps the most widely used in numerical analysis and have the advantage of forming a weil defined dass. The algorithms described here fall into two main categories, associated with the solution of linear systems and the algebraic eigenvalue problem respectively and each set is preceded by an introductory chapter giving a comparative assessment. In spite of the self-contained nature of the linear algebra field, experience has shown that even here the preparation of a fully tested set of algorithms is a far greater task than had been anticipated. Almost all the algorithms presented here have received pre-publication in Numerische Mathematik and the need to check very carefully whenever an algorithm
