Abstract
The Lanczos algorithms can be used to find a symmetric tridiagonal matrix from its eigenvalues and the first components of its normalized eigenvectors. The direct application of this method to discretized Strum-Liouville problems is useless since the finite difference eigenvalues behave quite differently asymptotically than the eigenvalues of the continuous Strum-Liouville problem. We suggest a multiplicative asymptotic correction for the discrete equation. The corrected equations can still be solved, at least approximately, by an algorithm similar to the Lanczos algorithm. Numerical experiments show that this approach leads to results of modest accuracy.
Information
Published: 1 January 1992
First available in Project Euclid: 18 November 2014
zbMATH: 0786.34025
MathSciNet: MR1210768
Rights: Copyright © 1992, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.
