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Mathematics of Computation

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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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Keywords: Eigenvalues, Lanczos algorithm, sparse symmetric matrices
Article copyright: © Copyright 1979 American Mathematical Society