Quantics Tensor Cross Interpolation for High-Resolution Parsimonious Representations of Multivariate Functions
PRL 132, 056501
| Authors/Editors: |
M. K. Ritter, Y. Núñez Fernández, M. Wallerberger, J. von Delft, H. Shinaoka, X. Waintal |
|---|---|
| Publication Date: | 2024 |
| Type of Publication: | Articles |
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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