Abstract
In this note we study a variant of the inverted Lanczos method which computes eigenvalue approximates of a symmetric matrix A as Ritz values of A from a Krylov space of A −1. The method turns out to be slightly faster than the Lanczos method at least as long as reorthogonalization is not required. The method is applied to the problem of determining the smallest eigenvalue of a symmetric Toeplitz matrix. It is accelerated taking advantage of symmetry properties of the correspond ng eigenvector.
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Voss, H. A Variant of the Inverted Lanczos Method. BIT Numerical Mathematics 41, 1111–1120 (2001). https://doi.org/10.1023/A:1021961900633
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DOI: https://doi.org/10.1023/A:1021961900633