# 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.identifier.uri http://hdl.handle.net/1903/568 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.language.iso 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 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
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