Estimates for the quantized tensor train ranks for the power functions
<|reference_start|>Estimates for the quantized tensor train ranks for the power functions: In this work we provide theoretical estimates for the ranks of the power functions $f(k) = k^{-\alpha}$, $\alpha>1$ in the quantized tensor train (QTT) format for $k = 1, 2, 3, \ldots, 2^{d}$. Such functions and their several generalizations (e.~g. $f(k) = k^{-\alpha} \cdot e^{-\lambda k}, \lambda > 0$) 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.<|reference_end|>
@article{matveev2024estimates,
    title={Estimates for the quantized tensor train ranks for the power functions},
    author={Sergey A. Matveev, Matvey Smirnov},
    journal={arXiv preprint arXiv:2404.12230},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.12230},
    primaryClass={math.NA cs.NA}
}