Matrix Iterative Analysis RICHARD S. VARGA Professor of Mathematics Case Institute of Technology PRENTICE-HALL, INC. Englewood Cliffs, New Jersey Matrix Iterative Analysis RICHARD S. VARGA Professor of Mathematics Case Institute of Technology PRENTICE-HALL, INC. Englewood Cliffs, New Jersey PRENTICE-HALL INTERNATIONAL, INC., London PRENTICE-HALL OF AUSTRALIA, PTY, LTD, Sydney PRENTICE-HALL OF CANADA, LTD, Toronto PRENTICE-HALL FRANCE, S.A.R.L. Paris PRENTICE-HALL OF JAPAN, INC, Tokyo PRENTICE-HALL DE MEXICO, S.A.. Mexico City Second printing August, 1963 © 1962 by Prentice-Hall, Inc. Englewood Cliffs, N. J. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. Library of Congress Catalog Number 62-21277 Printed in the United States of America 56550C To Esther PREFACE With the growth in speed and complexity of modern digital computers has come an increase in the use of computers by those who wish to find or approximate the solutions of partial differential equations in several vari- bles. This increasing use of computers for such problems has correspondingly interested many mathematicians in the underlying theory for that smaller branch of numerical analysis concerned with the efficient solution of matrix problems arising from discrete approximations to elliptic partial differential equations. This current interest has generated sufficient important mathematical contributions to warrant a survey of this mathematical theory. Accordingly, our first major aim is to survey the basic results pertaining to this topic. The basic material for this book is closely aligned with modern computing methods. The author was fortunate to have been associated with the Mathematics Group of the Bettis Atomic Power Laboratory where very large matrix problems (of order 20,000 in two dimensions!) are solved on fast computers in the d