Randomized Krylov-Schur eigensolver with deflation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911095866785792 |
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| author | de Damas, Jean-Guillaume Grigori, Laura |
| author_facet | de Damas, Jean-Guillaume Grigori, Laura |
| contents | This work introduces a novel algorithm to solve large-scale eigenvalue problems and seek a small set of eigenpairs. The method, called randomized Krylov-Schur (rKS), has a simple implementation and benefits from fast and efficient operations in low-dimensional spaces, such as sketch-orthogonalization processes and stable reordering of Schur factorizations. It also includes a practical deflation technique for converged eigenpairs, enabling the computation of the eigenspace associated with a given part of the spectrum. Numerical experiments are provided to demonstrate the scalability and accuracy of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Randomized Krylov-Schur eigensolver with deflation de Damas, Jean-Guillaume Grigori, Laura Numerical Analysis 65F15, 65F25, 65F50, 15B52 This work introduces a novel algorithm to solve large-scale eigenvalue problems and seek a small set of eigenpairs. The method, called randomized Krylov-Schur (rKS), has a simple implementation and benefits from fast and efficient operations in low-dimensional spaces, such as sketch-orthogonalization processes and stable reordering of Schur factorizations. It also includes a practical deflation technique for converged eigenpairs, enabling the computation of the eigenspace associated with a given part of the spectrum. Numerical experiments are provided to demonstrate the scalability and accuracy of the method. |
| title | Randomized Krylov-Schur eigensolver with deflation |
| topic | Numerical Analysis 65F15, 65F25, 65F50, 15B52 |
| url | https://arxiv.org/abs/2508.05400 |