On the low-rank approximation by the pivoted Cholesky decomposition

Authors:
Helmut Harbrecht;Michael Peters;Reinhold Schneider
Affiliations:
Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland;Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland;Institut für Mathematik, Technische Universität Berlin, Straíe des 17. Juni 136, 10623 Berlin, Germany
Venue:
Applied Numerical Mathematics
Year:
2012

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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.