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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

How to make the Lanczos algorithm converge slowly


Author: D. S. Scott
Journal: Math. Comp. 33 (1979), 239-247
MSC: Primary 65F15
MathSciNet review: 514821
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Abstract: The Paige style Lanczos algorithm is an iterative method for finding a few eigenvalues of large sparse symmetric matrices. Some beautiful relationships among the elements of the eigenvectors of a symmetric tridiagonal matrix are used to derive a perverse starting vector which delays convergence as long as possible. Why such slow convergence is never seen in practice is also examined.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1979-0514821-5
PII: S 0025-5718(1979)0514821-5
Keywords: Eigenvalues, Lanczos algorithm, sparse symmetric matrices
Article copyright: © Copyright 1979 American Mathematical Society