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Estimates for the quantized tensor train ranks for the power functions
Published 18 Apr 2024 in math.NA and cs.NA | (2404.12230v1)
Abstract: 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.
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