Estimation of QTT Ranks of Regular Functions on a Uniform Square Grid
-
Published:2024-02
Issue:2
Volume:64
Page:177-187
-
ISSN:0965-5425
-
Container-title:Computational Mathematics and Mathematical Physics
-
language:en
-
Short-container-title:Comput. Math. and Math. Phys.
Author:
Zyl’ A.,Zamarashkin N.
Publisher
Pleiades Publishing Ltd
Reference8 articles.
1. L. Vysotsky, “TT ranks of approximate tensorizations of some smooth functions,” Comput. Math. Math. Phys. 61 (5), 750–760 (2021).
2. L. Vysotsky and M. Rakhuba, “Tensor rank bounds and explicit QTT representations for the inverses of circulant matrices,” Numer. Linear Algebra Appl. 30 (3), e2461 (2023).
3. A. Chertkov, I. Oseledets, and M. Rakhuba, “Robust discretization in quantized tensor train format for elliptic problems in two dimensions” (2016). https://doi.org/10.48550/arXiv.1612.01166
4. V. Kazeev and B. Khoromskij, “Low-rank explicit QTT representation of the Laplace operator and its inverse,” SIAM J. Matrix Anal. Appl. 33 (3), 742–758 (2012).
5. I. Oseledets and E. Tyrtyshnikov, “TT-cross approximation for multidimensional arrays,” Linear Algebra Appl. 432 (1), 70–88 (2010).