A fast randomized algorithm for overdetermined linear least-squares regression
We introduce a randomized algorithm for overdetermined linear least-squares regression. Given an arbitrary full-rank m x n matrix A with m >/= n, any m x 1 vector b, and any positive real number epsilon, the procedure computes an n x 1 vector x such that x minimizes the Euclidean norm ||Ax - b ||...
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| Vydáno v: | Proceedings of the National Academy of Sciences - PNAS Ročník 105; číslo 36; s. 13212 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
United States
09.09.2008
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| Témata: | |
| ISSN: | 1091-6490, 1091-6490 |
| On-line přístup: | Zjistit podrobnosti o přístupu |
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| Shrnutí: | We introduce a randomized algorithm for overdetermined linear least-squares regression. Given an arbitrary full-rank m x n matrix A with m >/= n, any m x 1 vector b, and any positive real number epsilon, the procedure computes an n x 1 vector x such that x minimizes the Euclidean norm ||Ax - b || to relative precision epsilon. The algorithm typically requires ((log(n)+log(1/epsilon))mn+n(3)) floating-point operations. This cost is less than the (mn(2)) required by the classical schemes based on QR-decompositions or bidiagonalization. We present several numerical examples illustrating the performance of the algorithm. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 1091-6490 1091-6490 |
| DOI: | 10.1073/pnas.0804869105 |