 Dynamical low-rank approximation: applications and numerical experimentsAchim Nonnenmacher and Christian Lubich Mathematics and Computers in Simulation (MATCOM), 2008, vol. 79, issue 4, 1346-1357 Abstract: Dynamical low-rank approximation is a differential-equation-based approach to efficiently compute low-rank approximations to time-dependent large data matrices or to solutions of large matrix differential equations. We illustrate its use in the following application areas: as an updating procedure in latent semantic indexing for information retrieval, in the compression of series of images, and in the solution of time-dependent partial differential equations, specifically on a blow-up problem of a reaction-diffusion equation in two and three spatial dimensions. In 3D and higher dimensions, space discretization yields a tensor differential equation whose solution is approximated by low-rank tensors, effectively solving a system of discretized partial differential equations in one spatial dimension. Keywords: Dynamical low-rank approximation; Differential equations; Model reduction; Latent semantic indexing; Image compression; Blow-up; Tensor approximation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2008:i:4:p:1346-1357 DOI: 10.1016/j.matcom.2008.03.007 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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