Error Analysis of the Quasi-Gram--Schmidt Algorithm
| dc.contributor.author | Stewart, G. W. | en_US |
| dc.date.accessioned | 2004-05-31T23:36:45Z | |
| dc.date.available | 2004-05-31T23:36:45Z | |
| dc.date.created | 2004-03 | en_US |
| dc.date.issued | 2004-04-19 | en_US |
| dc.description.abstract | Let the $n{\times}p$ $(n\geq p)$ matrix $X$ have the QR~factorization $X = QR$, where $R$ is an upper triangular matrix of order $p$ and $Q$ is orthonormal. This widely used decomposition has the drawback that $Q$ is not generally sparse even when $X$ is. One cure is to discard $Q$ retaining only $X$ and $R$. Products like $a = Q\trp y = R\itp X\trp y$ can then be formed by computing $b = X\trp y$ and solving the system $R\trp a = b$. This approach can be used to modify the Gram--Schmidt algorithm for computing $Q$ and $R$ to compute $R$ without forming $Q$ or altering $X$. Unfortunately, this quasi-Gram--Schmidt algorithm can produce inaccurate results. In this paper it is shown that with reorthogonalization the inaccuracies are bounded under certain natural conditions. (UMIACS-TR-2004-17) | en_US |
| dc.format.extent | 195881 bytes | |
| dc.format.mimetype | application/postscript | |
| dc.identifier.uri | http://hdl.handle.net/1903/1346 | |
| dc.language.iso | en_US | |
| dc.relation.isAvailableAt | Digital Repository at the University of Maryland | en_US |
| dc.relation.isAvailableAt | University of Maryland (College Park, Md.) | en_US |
| dc.relation.isAvailableAt | Tech Reports in Computer Science and Engineering | en_US |
| dc.relation.isAvailableAt | UMIACS Technical Reports | en_US |
| dc.relation.ispartofseries | UM Computer Science Department; CS-TR-4572 | en_US |
| dc.relation.ispartofseries | UMIACS; UMIACS-TR-2004-17 | en_US |
| dc.title | Error Analysis of the Quasi-Gram--Schmidt Algorithm | en_US |
| dc.type | Technical Report | en_US |