How to make the Lanczos algorithm converge slowly

Scott, D. S.

doi:10.1090/S0025-5718-1979-0514821-5

How to make the Lanczos algorithm converge slowly
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by D. S. Scott PDF

Math. Comp. 33 (1979), 239-247 Request permission

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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