Faster SVD for Matrices with Small $m/n$
| dc.contributor.author | Bau, David | en_US |
| dc.date.accessioned | 2007-04-23T16:35:00Z | |
| dc.date.available | 2007-04-23T16:35:00Z | |
| dc.date.issued | 1994-03 | en_US |
| dc.description.abstract | The singular values of a matrix are conventionally computed using either the bidiagonalization algorithm by Golub and Reinsch (1970) when $m/n less than 5/3$, or the algorithm by Lawson and Hanson (1974) and Chan (1982) when $m/n greater than 5/3.$ However, there is an algorithm that is faster and that does not involve a discontinuous choice, as follows: in all cases, perform a QR factorization as in Lawson-Hanson-Chan, but rather than do this right at the beginning, do it after zeros have already been introduced in the first $j = 2n - m$ rows and columns. The same technique applies when computing singular vectors, with one small modification. If left singular vectors are needed, the new algorithm becomes advantageous only when $m greater than 1.2661n$, and the best $j$ in this case is $3n - m$. The benefits of the new algorithm appear in terms of classical scalar floating-point operation counts; the effects of locality and parallelization are not considered in the analysis. | en_US |
| dc.format.extent | 721871 bytes | |
| dc.format.extent | 285462 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.format.mimetype | application/postscript | |
| dc.identifier.citation | http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR94-1414 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1813/6196 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Cornell University | en_US |
| dc.subject | computer science | en_US |
| dc.subject | technical report | en_US |
| dc.title | Faster SVD for Matrices with Small $m/n$ | en_US |
| dc.type | technical report | en_US |