Truncation of Tensors in the Hierarchical Format

Wolfgang Hackbusch

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Submission date: 09. Apr. 2018
Pages: 16
published in: SeMA journal : boletin Sociedad Espaõnola de la Matemática Aplicada (2019), pp not yet known
DOI number (of the published article): 10.1007/s40324-018-00184-5
Bibtex
MSC-Numbers: 15A69, 15A18, 15A99, 65F99, 65T99
Keywords and phrases: hierarchical tensor representation, HOSVD truncation
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Abstract:
Tensors are in general large-scale data which require a special representation. These representations are also called a format. After mentioning the r-term and tensor subspace formats, we describe the hierarchical tensor format which is the most flexible one. Since operations with tensors often produce tensors of larger memory cost, truncation to reduced ranks is of utmost importance. The so-called higher-order singular-value decomposition (HOSVD) provides a save truncation with explicit error control. The paper explains in detail how the HOSVD procedure is performed within the hierarchical tensor format. Finally, we state special favourable properties of the HOSVD truncation.