On Estimating the Largest Eigenvalue with the Lanczos Algorithm
- 1 January 1982
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 38 (157) , 153-165
- https://doi.org/10.2307/2007471
Abstract
The Lanczos algorithm applied to a positive definite matrix produces good approximations to the eigenvalues at the extreme ends of the spectrum after a few iterations. In this note we utilize this behavior and develop a simple algorithm which computes the largest eigenvalue. The algorithm is especially economical if the order of the matrix is large and the accuracy requirements are low. The phenomenon of misconvergence is discussed. Some simple extensions of the algorithm are also indicated. Finally, some numerical examples and a comparison with the power method are given.Keywords
This publication has 3 references indexed in Scilit:
- The Symmetric Eigenvalue ProblemJournal of Applied Mechanics, 1981
- Tracking the Progress of the Lanczos Algorithm for Large Symmetric EigenproblemsIMA Journal of Numerical Analysis, 1981
- Estimating the Largest Eigenvalue of a Positive Definite MatrixMathematics of Computation, 1979