Papers › Low-rank tensor structure preservation in fractional operators by means of exponential sums
Low-rank tensor structure preservation in fractional operators by means of exponential sums
Angelo A. Casulli, Leonardo Robol
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
The use of fractional differential equations is a key tool in modeling non-local phenomena. Often, an efficient scheme for solving a linear system involving the discretization of a fractional operator is evaluating the matrix function x = 𝒜^(-α) c, where 𝒜 is a discretization of the classical Laplacian, and α a fractional exponent between $0$ and $1$. In this work, we derive an exponential sum approximation for f(z) =z^(-α) that is accurate over [1, ∞) and allows to efficiently approximate the action of bounded and unbounded operators of this kind on tensors stored in a variety of low-rank formats (CP, TT, Tucker). The results are relevant from a theoretical perspective as well, as they predict the low-rank approximability of the solutions of these linear systems in low-rank tensor formats.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections