On the low-rank approximation by the pivoted Cholesky decomposition

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• 作者：Helmut Harbrecht^a ; ^{helmut.harbrecht@unibas.ch} ; Michael Peters^a ; ^{michael.peters@unibas.ch} ; Reinhold Schneider^b ; ^{schneidr@math.tu-berlin.de}
• 关键词：Low-rank approximation ; Cholesky decomposition
• 刊名：Applied Numerical Mathematics
• 出版年：2012
• 期刊代码：8_01689274
• 类别：cp
• 出版时间：April, 2012
• 卷：62
• 期：4
• 页码：428-440
• 文件大小：632 K

摘要

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.