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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2401.11786 |
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| _version_ | 1866910304655376384 |
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| author | Shao, Nian Chen, Wenbin Bai, Zhaojun |
| author_facet | Shao, Nian Chen, Wenbin Bai, Zhaojun |
| contents | This paper is concerned with the extraction of the smallest eigenvalue and the corresponding eigenvector of a symmetric positive definite matrix pencil. We reveal implicit convexity of the eigenvalue problem in Euclidean space. A provable accelerated eigensolver based on preconditioning and implicit convexity (EPIC) is proposed. Theoretical analysis shows the acceleration of EPIC with the rate of convergence resembling the expected rate of convergence of the well-known locally optimal preconditioned conjugate gradient (LOPCG). A complete proof of the expected rate of convergence of LOPCG is elusive so far. Numerical results confirm our theoretical findings of EPIC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11786 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | EPIC: a provable accelerated Eigensolver based on Preconditioning and Implicit Convexity Shao, Nian Chen, Wenbin Bai, Zhaojun Numerical Analysis 15A08, 65F08, 65F15, 90C25 This paper is concerned with the extraction of the smallest eigenvalue and the corresponding eigenvector of a symmetric positive definite matrix pencil. We reveal implicit convexity of the eigenvalue problem in Euclidean space. A provable accelerated eigensolver based on preconditioning and implicit convexity (EPIC) is proposed. Theoretical analysis shows the acceleration of EPIC with the rate of convergence resembling the expected rate of convergence of the well-known locally optimal preconditioned conjugate gradient (LOPCG). A complete proof of the expected rate of convergence of LOPCG is elusive so far. Numerical results confirm our theoretical findings of EPIC. |
| title | EPIC: a provable accelerated Eigensolver based on Preconditioning and Implicit Convexity |
| topic | Numerical Analysis 15A08, 65F08, 65F15, 90C25 |
| url | https://arxiv.org/abs/2401.11786 |