Structure Preserving Restarts of the Non-Symmetric Lanczos Algorithm via the Implicitly shifted LR algorithm

Prabal S. Negi; Cristobal Arratia

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arXiv · 2407.06561

Structure Preserving Restarts of the Non-Symmetric Lanczos Algorithm via the Implicitly shifted LR algorithm

Prabal S. Negi·Cristobal Arratia

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Abstract

The implicitly shifted QR iteration is used as a restart procedure for the Arnoldi method for the calculation of a few dominant eigenvalues of a large matrix. We show that the underlying idea of implicit polynomial filtering can be utilized in much the same manner via the implicitly shifted LR iteration to create a restart procedure for the non-symmetric Lanczos algorithm for eigenvalue computations, which preserves the tri-diagonal structure of the reduced matrix.

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Prabal S. Negi, Cristobal Arratia. 2024-07-09. Structure Preserving Restarts of the Non-Symmetric Lanczos Algorithm via the Implicitly shifted LR algorithm. https://arxiv.org/abs/2407.06561

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