A DEIM Induced CUR Factorization
| dc.citation.firstpage | A1454 | |
| dc.citation.issueNumber | 3 | |
| dc.citation.journalTitle | SIAM Journal on Scientific Computing | |
| dc.citation.lastpage | A1482 | |
| dc.citation.volumeNumber | 38 | |
| dc.contributor.author | Sorensen, D.C. | |
| dc.contributor.author | Embree, Mark | |
| dc.date.accessioned | 2017-05-15T21:11:38Z | |
| dc.date.available | 2017-05-15T21:11:38Z | |
| dc.date.issued | 2016 | |
| dc.description.abstract | We derive a CUR approximate matrix factorization based on the discrete empirical interpolation method (DEIM). For a given matrix ${\bf A}$, such a factorization provides a low-rank approximate decomposition of the form ${\bf A} \approx \bf C \bf U \bf R$, where ${\bf C}$ and ${\bf R}$ are subsets of the columns and rows of ${\bf A}$, and ${\bf U}$ is constructed to make $\bf C\bf U \bf R $ a good approximation. Given a low-rank singular value decomposition ${\bf A} \approx \bf V \bf S \bf W^T$, the DEIM procedure uses ${\bf V}$ and ${\bf W}$ to select the columns and rows of ${\bf A}$ that form ${\bf C}$ and ${\bf R}$. 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 ${\bf V}$ and ${\bf W}$. For very large problems, ${\bf V}$ and ${\bf W}$ can be approximated well using an incremental QR algorithm that makes only one pass through ${\bf A}$. Numerical examples illustrate the favorable performance of the DEIM-CUR method compared to CUR approximations based on leverage scores. | |
| dc.identifier.citation | Sorensen, D.C. and Embree, Mark. "A DEIM Induced CUR Factorization." <i>SIAM Journal on Scientific Computing,</i> 38, no. 3 (2016) SIAM: A1454-A1482. http://dx.doi.org/10.1137/140978430. | |
| dc.identifier.doi | http://dx.doi.org/10.1137/140978430 | |
| dc.identifier.uri | https://hdl.handle.net/1911/94281 | |
| dc.language.iso | eng | |
| dc.publisher | SIAM | |
| dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | |
| dc.subject.keyword | discrete empirical interpolation method | |
| dc.subject.keyword | CUR factorization | |
| dc.subject.keyword | pseudoskeleton de-composition | |
| dc.subject.keyword | low-rank approximation | |
| dc.subject.keyword | one-pass QR decomposition | |
| dc.title | A DEIM Induced CUR Factorization | |
| dc.type | Journal article | |
| dc.type.dcmi | Text | |
| dc.type.publication | publisher version |
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