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A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds


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Title: A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds
Authors : Billaud Friess, Marie
Falcó Montesinos, Antonio
Nouy, Anthony
Keywords: Grassmann manifolds.Grassmann, Variedades de.Geometría diferencial.Geometry, Differential.Manifolds (Mathematics)Differential topology.Topología diferencial.Variedades (Matemáticas)
Publisher: Springer Nature
Citation: Billaud-Friess, M., Falcó, A. & Nouy, A. (2022). A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds. BIT Numerical Mathematics, vol. 62, i. 2 (jun.), pp. 387-408. DOI: https://doi.org/10.1007/s10543-021-00884-x
Abstract: In this paper, we propose a new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of the set of fixed rank matrices. We first introduce a geometric description of the set of fixed rank matrices which relies on a natural parametrization of matrices. More precisely, it is endowed with the structure of analytic principal bundle, with an explicit description of local charts. For matrix differential equations, we introduce a first order numerical integrator working in local coordinates. The resulting algorithm can be interpreted as a particular splitting of the projection operator onto the tangent space of the low-rank matrix manifold. It is proven to be exact in some particular case. Numerical experiments confirm this result and illustrate the robustness of the proposed algorithm.
Description: Este artículo se encuentra disponible en la siguiente URL: https://link.springer.com/article/10.1007/s10543-021-00884-x
Este es el postprint del siguiente artículo: Billaud-Friess, M., Falcó, A. & Nouy, A. (2022). A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds. Bit Numerical Mathematics, vol. 62, i. 2 (jun.), pp. 387?408, que se ha publicado de forma definitiva en https://doi.org/10.1007/s10543-021-00884-x
This is the peer reviewed version of the following article: Billaud-Friess, M., Falcó, A. & Nouy, A. (2022). A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds. Bit Numerical Mathematics, vol. 62, i. 2 (jun.), pp. 387?408, which has been published in final form at https://doi.org/10.1007/s10543-021-00884-x
URI: http://hdl.handle.net/10637/13934
Rights : http://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
ISSN: 0006-3835
1572-9125 (Electrónico)
Issue Date: 30-Jun-2022
Center : Universidad Cardenal Herrera-CEU
Appears in Collections:Dpto. Matemáticas, Física y Ciencias Tecnológicas





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