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.
