The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Algorithms for Numerical Analysis in High Dimensions
Abstract
Nearly every numerical analysis algorithm has computational complexity that scales exponentially in the underlying physical dimension. The separated representation, introduced previously, allows many operations to be performed with scaling that is formally linear in the dimension. In this paper we further develop this representation by (i) discussing the variety of mechanisms that allow it to be surprisingly efficient; (ii) addressing the issue of conditioning; (iii) presenting algorithms for solving linear systems within this framework; and (iv) demonstrating methods for dealing with antisymmetric functions, as arise in the multiparticle Schrödinger equation in quantum mechanics. Numerical examples are given.
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Cites
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505
Cited by
Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition
Oseledets, I. V. (2010) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/090757861 · Cited by 174
Metadata
- Authors
- Beylkin, G., & Mohlenkamp, M. J.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 2005-01
- Volume
- 26
- Issue
- 6
- Pages
- 2133-2159
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W2073469810
- Cited by
- 352
- References
- 1
- FWCI
- 3.80
- Type
- journal article
- Language
- en
- Open access
- closed
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- Beylkin, G., & Mohlenkamp, M. J. (2005). Algorithms for Numerical Analysis in High Dimensions. SIAM Journal on Scientific Computing. https://doi.org/10.1137/040604959
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
