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dc.contributor.authorSorensen, D.C.
Embree, M.
dc.date.accessioned 2018-06-19T17:49:27Z
dc.date.available 2018-06-19T17:49:27Z
dc.date.issued 2014-07
dc.identifier.citation Sorensen, D.C. and Embree, M.. "A DEIM Induced CUR Factorization." (2014) https://hdl.handle.net/1911/102226.
dc.identifier.urihttps://hdl.handle.net/1911/102226
dc.description.abstract We derive a CUR matrix factorization based on the Discrete Empirical Interpolation Method (DEIM). For a given matrix A, such a factorization provides a low rank approximate decomposition of the form A ≈ CUR, where C and R are subsets of the columns and rows of A, and U is constructed to make CUR a good approximation. Given a low-rank singular value decomposition A ≈ VSWT, the DEIM procedure uses V and W to select the columns and rows of A that form C and R. Through an error analysis applicable to a general class of CUR factorizations, we show that the accuracy tracks the optimal approximation error within a factor that depends on the conditioning of submatrices of V and W. For large-scale problems, V and W can be approximated using an incremental QR algorithm that makes one pass through A. Numerical examples illustrate the favorable performance of the DEIM-CUR method, compared to CUR approximations based on leverage scores.
dc.format.extent 30 pp
dc.title A DEIM Induced CUR Factorization
dc.type Technical report
dc.date.note July 2014, revised September 2015
dc.identifier.digital TR14-04
dc.type.dcmi Text


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