RUS  ENG
Full version
JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2024 Volume 64, Number 2, Pages 189–199 (Mi zvmmf11698)

General numerical methods

Estimation of QTT ranks of regular functions on a uniform square grid

A. V. Zylab, N. L. Zamarashkina

a Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia
b Moscow Institute of Physics and Technology, 141701, Dolgoprudny, Moscow oblast, Russia

Abstract: The paper proves estimates of $\varepsilon$-ranks for TT decompositions of tensors obtained by tensorizing the values of a regular function of one complex variable on a uniform square grid in the complex plane. A relation between the approximation accuracy and the geometry of the domain of regularity of the function is established.

Key words: tensor train, QTT, rank estimation of TT approximations, regular functions.

UDC: 519.651

Received: 10.07.2023
Revised: 10.07.2023
Accepted: 20.10.2023

DOI: 10.31857/S0044466924020017


 English version:
Computational Mathematics and Mathematical Physics, 2024, 64:2, 177–187

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2026