Estimates for the quantized tensor train ranks for the power functions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909458964152320 |
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| author | Matveev, Sergey A. Smirnov, Matvey |
| author_facet | Matveev, Sergey A. Smirnov, Matvey |
| contents | In this work we provide theoretical estimates for the ranks of the power functions $f(k) = k^{-α}$, $α>1$ in the quantized tensor train (QTT) format for $k = 1, 2, 3, \ldots, 2^{d}$. Such functions and their several generalizations (e.~g. $f(k) = k^{-α} \cdot e^{-λk}, λ> 0$) play an important role in studies of the asymptotic solutions of the aggregation-fragmentation kinetic equations. In order to support the constructed theory we verify the values of QTT-ranks of these functions in practice with the use of the TTSVD procedure and show an agreement between the numerical and analytical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Estimates for the quantized tensor train ranks for the power functions Matveev, Sergey A. Smirnov, Matvey Numerical Analysis 15A18, 15A69, 65F55 G.1.3; G.1.2 In this work we provide theoretical estimates for the ranks of the power functions $f(k) = k^{-α}$, $α>1$ in the quantized tensor train (QTT) format for $k = 1, 2, 3, \ldots, 2^{d}$. Such functions and their several generalizations (e.~g. $f(k) = k^{-α} \cdot e^{-λk}, λ> 0$) play an important role in studies of the asymptotic solutions of the aggregation-fragmentation kinetic equations. In order to support the constructed theory we verify the values of QTT-ranks of these functions in practice with the use of the TTSVD procedure and show an agreement between the numerical and analytical results. |
| title | Estimates for the quantized tensor train ranks for the power functions |
| topic | Numerical Analysis 15A18, 15A69, 65F55 G.1.3; G.1.2 |
| url | https://arxiv.org/abs/2404.12230 |