估计均匀正方形网格上正则函数的 QTT 等级

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。

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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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