On a New Way of Solving the Linear Equations that Arise in the Method of Least Squares
| dc.contributor.author | Jacobi, C. G. | en_US |
| dc.contributor.author | Stewart, G. W. | en_US |
| dc.date.accessioned | 2004-05-31T22:22:15Z | |
| dc.date.available | 2004-05-31T22:22:15Z | |
| dc.date.created | 1992-05 | en_US |
| dc.date.issued | 1998-10-15 | en_US |
| dc.description.abstract | Translated by G. W. Stewart This report contains a translation of a paper of C. G. J. Jacobi, ``Ueber eine neue Aufl\"osungsart der bei der Methode der kleinsten Quadrate vorkommenden line\"aren Gleichungen,'' which appeared in {\it Astronomische Nachrichten\/} {\bf 22} (1845). In the paper Jacobi shows how to use rotations to increase the diagonal dominance of symmetric linear systems, which he then solves by what we today call the point Jacobi method. This preconditioner is none other than Jacobi's method for diagonalizing a symmetric matrix. Although Jacobi points out his method can be used to find eigenvalues, he reserves a fuller exposition for a later paper [Journal f\"ur die reine und angewandte Mathematik, {\bf 30} (1846), 51--s94], which is now generally cited as the source of the method. A variant for unsymmetric equations is also considered. (Also cross-referenced as UMIACS-TR-92-42) | en_US |
| dc.format.extent | 110016 bytes | |
| dc.format.mimetype | application/postscript | |
| dc.identifier.uri | http://hdl.handle.net/1903/568 | |
| 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-2877 | en_US |
| dc.relation.ispartofseries | UMIACS; UMIACS-TR-92-42 | en_US |
| dc.title | On a New Way of Solving the Linear Equations that Arise in the Method of Least Squares | en_US |
| dc.type | Technical Report | en_US |