Truncation of tensors in the hierarchical format

Wolfgang Hackbusch ^[1]
1. [1] Max-Planck-Institut Mathematik in den Naturwissenschaften
Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 78, Nº. Extra 2, 2021, págs. 175-192
Idioma: inglés
DOI: 10.1007/s40324-018-00184-5
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Resumen
- 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.