A DEIM Induced CUR Factorization
| dc.contributor.author | Sorensen, D.C. | en_US |
| dc.contributor.author | Embree, M. | en_US |
| dc.date.accessioned | 2018-06-19T17:49:27Z | en_US |
| dc.date.available | 2018-06-19T17:49:27Z | en_US |
| dc.date.issued | 2014-07 | en_US |
| dc.date.note | July 2014, revised September 2015 | en_US |
| 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. | en_US |
| dc.format.extent | 30 pp | en_US |
| dc.identifier.citation | Sorensen, D.C. and Embree, M.. "A DEIM Induced CUR Factorization." (2014) <a href="https://hdl.handle.net/1911/102226">https://hdl.handle.net/1911/102226</a>. | en_US |
| dc.identifier.digital | TR14-04 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/102226 | en_US |
| dc.language.iso | eng | en_US |
| dc.title | A DEIM Induced CUR Factorization | en_US |
| dc.type | Technical report | en_US |
| dc.type.dcmi | Text | en_US |
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