Tree-based tensor formats

被引：0
作者：
Falcó A. [1 ]
Hackbusch W. [2 ]
Nouy A. [3 ]
机构：
[1] ESI International Chair@CEU-UCH, Departamento de Matemáticas, Física y Ciencias Tecnológicas, Universidad Cardenal Herrera-CEU, CEU Universities, San Bartolomé 55, Alfara del Patriarca, 46115, Valencia
[2] Max-Planck-Institut Mathematik in den Naturwissenschaften, Inselstr. 22, Leipzig
[3] Centrale Nantes, LMJL UMR CNRS 6629, 1 rue de la Noë, Nantes Cedex 3
来源：
SeMA Journal | 2021年 / 78卷 / 2期
关键词：
Best approximation; Tensor spaces; Tree-based rank; Tree-based tensor format;
D O I：
10.1007/s40324-018-0177-x
中图分类号：
学科分类号：
摘要：
The main goal of this paper is to study the topological properties of tensors in tree-based Tucker format. These formats include the Tucker format and the Hierarchical Tucker format. A property of the so-called minimal subspaces is used for obtaining a representation of tensors with either bounded or fixed tree-based rank in the underlying algebraic tensor space. We provide a new characterisation of minimal subspaces which extends the existing characterisations. We also introduce a definition of topological tensor spaces in tree-based format, with the introduction of a norm at each vertex of the tree, and prove the existence of best approximations from sets of tensors with bounded tree-based rank, under some assumptions on the norms weaker than in the existing results. © 2018, Sociedad Española de Matemática Aplicada.
引用
收藏
页码：159 / 173
页数：14
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