估计均匀正方形网格上正则函数的 QTT 等级

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Computational Mathematics and Mathematical Physics Pub Date : 2024-04-01 DOI:10.1134/s0965542524020143

A. Zyl’, N. Zamarashkin

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引用次数: 0

摘要

摘要本文证明了通过在复平面上的均匀正方形网格上张量一个正则复变函数的值而得到的张量的 TT 分解的 \(\varepsilon \)-ranks估计值。建立了近似精度与函数正则域几何之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Estimation of QTT Ranks of Regular Functions on a Uniform Square Grid

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.

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来源期刊

Computational Mathematics and Mathematical Physics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.50

自引率

14.30%

发文量

125

审稿时长

4-8 weeks

期刊介绍： Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.