Momentum accelerated power iterations and the restarted Lanczos method
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910036331069440 |
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| author | Barletta, Alessandro Marshall, Nicholas Pollock, Sara |
| author_facet | Barletta, Alessandro Marshall, Nicholas Pollock, Sara |
| contents | In this paper we compare two methods for finding extremal eigenvalues and eigenvectors: the restarted Lanczos method and momentum accelerated power iterations. The convergence of both methods is based on ratios of Chebyshev polynomials evaluated at subdominant and dominant eigenvalues; however, the convergence is not the same. Here we compare the theoretical convergence properties of both methods, and determine the relative regimes where each is more efficient. We further introduce a preconditioning technique for the restarted Lanczos method using momentum accelerated power iterations, and demonstrate its effectiveness. The theoretical results are backed up by numerical tests on benchmark problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Momentum accelerated power iterations and the restarted Lanczos method Barletta, Alessandro Marshall, Nicholas Pollock, Sara Numerical Analysis 65F15, 65F08 In this paper we compare two methods for finding extremal eigenvalues and eigenvectors: the restarted Lanczos method and momentum accelerated power iterations. The convergence of both methods is based on ratios of Chebyshev polynomials evaluated at subdominant and dominant eigenvalues; however, the convergence is not the same. Here we compare the theoretical convergence properties of both methods, and determine the relative regimes where each is more efficient. We further introduce a preconditioning technique for the restarted Lanczos method using momentum accelerated power iterations, and demonstrate its effectiveness. The theoretical results are backed up by numerical tests on benchmark problems. |
| title | Momentum accelerated power iterations and the restarted Lanczos method |
| topic | Numerical Analysis 65F15, 65F08 |
| url | https://arxiv.org/abs/2511.05364 |