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On the low-rank approximation by the pivoted Cholesky decomposition

Harbrecht, Helmut and Peters, Michael and Schneider, Reinhold. (2012) On the low-rank approximation by the pivoted Cholesky decomposition. Applied numerical mathematics, Vol. 62, H. 4. pp. 428-440.

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Official URL: http://edoc.unibas.ch/dok/A6002534

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Abstract

The present paper is dedicated to the application of the pivoted Cholesky decomposition to compute low-rank approximations of dense, positive semi-definite matrices.The resulting truncation error is rigorously controlled in terms of the trace norm. Exponential convergence rates are proved under the assumption that the eigenvalues of the matrix under consideration exhibit a sufficiently fast exponential decay. By numerical experiments it is demonstrated that the pivoted Cholesky decomposition leads to very efficient algorithms to separate the variables of bi-variate functions.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut and Peters, Michael
Item Type:Article, refereed
Article Subtype:Research Article
Bibsysno:Link to catalogue
Publisher:Elsevier
ISSN:0168-9274
Note:Publication type according to Uni Basel Research Database: Journal article
Last Modified:08 Nov 2012 16:22
Deposited On:08 Nov 2012 16:14

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