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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.08265 |
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| _version_ | 1866915471938289664 |
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| author | Yun, Ho Panaretos, Victor M. |
| author_facet | Yun, Ho Panaretos, Victor M. |
| contents | We introduce the Tensorized-and-Restricted Krylov (TReK) method, a simple and efficient algorithm for estimating covariance tensors with large observational sizes. TReK extends the conjugate gradient method to incorporate range restrictions, enabling its use in a variety of covariance smoothing applications. By leveraging matrix-level operations, it achieves significant improvements in both computational speed and memory cost, improving over existing methods by an order of magnitude. TReK ensures finite-step convergence in the absence of rounding errors and converges fast in practice, making it well-suited for large-scale problems. The algorithm is also highly flexible, supporting a wide range of forward and projection tensors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08265 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast and Cheap Krylov-Based Covariance Smoothing Yun, Ho Panaretos, Victor M. Computation Applications 65D10 (Primary) 62G05 (Secondary) We introduce the Tensorized-and-Restricted Krylov (TReK) method, a simple and efficient algorithm for estimating covariance tensors with large observational sizes. TReK extends the conjugate gradient method to incorporate range restrictions, enabling its use in a variety of covariance smoothing applications. By leveraging matrix-level operations, it achieves significant improvements in both computational speed and memory cost, improving over existing methods by an order of magnitude. TReK ensures finite-step convergence in the absence of rounding errors and converges fast in practice, making it well-suited for large-scale problems. The algorithm is also highly flexible, supporting a wide range of forward and projection tensors. |
| title | Fast and Cheap Krylov-Based Covariance Smoothing |
| topic | Computation Applications 65D10 (Primary) 62G05 (Secondary) |
| url | https://arxiv.org/abs/2501.08265 |