Quantics Tensor Cross Interpolation for High-Resolution Parsimonious Representations of Multivariate Functions
Multivariate functions of continuous variables arise in countless branches of science. Numerical computations with such functions typically involve a compromise between two contrary desiderata: accurate resolution of the functional dependence, versus parsimonious memory usage. Recently, two promisin...
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| Veröffentlicht in: | Physical review letters Jg. 132; H. 5; S. 056501 |
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| Hauptverfasser: | , , , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
United States
American Physical Society
02.02.2024
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| Schlagworte: | |
| ISSN: | 0031-9007, 1079-7114, 1079-7114 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Multivariate functions of continuous variables arise in countless branches of science. Numerical computations with such functions typically involve a compromise between two contrary desiderata: accurate resolution of the functional dependence, versus parsimonious memory usage. Recently, two promising strategies have emerged for satisfying both requirements: (i) The quantics representation, which expresses functions as multi-index tensors, with each index representing one bit of a binary encoding of one of the variables; and (ii) tensor cross interpolation (TCI), which, if applicable, yields parsimonious interpolations for multi-index tensors. Here, we present a strategy, quantics TCI, which combines the advantages of both schemes. We illustrate its potential with an application from condensed matter physics: the computation of Brillouin zone integrals. |
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| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 0031-9007 1079-7114 1079-7114 |
| DOI: | 10.1103/PhysRevLett.132.056501 |