## Re: [Algorithms] finding eigenvectors of large symmetric matrices

 Re: [Algorithms] finding eigenvectors of large symmetric matrices From: Michael Walter - 2007-10-23 18:38:19 ```Hi, the QR algorithm should work well (when preprocessing your matrix to upper Hessenberg form, you could use e.g. Givens rotations in order to exploit sparseness of your matrix) and gives the full set of eigenvectors. Regards, Michael On 10/23/07, Sam Martin wrote: > > > > > Hi, > > > > Anyone familiar with any numerical techniques for finding the eigenvectors > of very large but sparse symmetric matrices, or just large dense symmetric > matrices? Things like a big covariance matrix, or an undirected graph. > > > > Seems like a very large field so if anyone has any pointers on what's > particularly worth looking at I'd appreciate it. > > > > Cheers, > > Sam > > > > > > > ------------------------------------------------------------------------- > This SF.net email is sponsored by: Splunk Inc. > Still grepping through log files to find problems? Stop. > Now Search log events and configuration files using AJAX and a browser. > Download your FREE copy of Splunk now >> http://get.splunk.com/ > _______________________________________________ > GDAlgorithms-list mailing list > GDAlgorithms-list@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list > ```

 [Algorithms] finding eigenvectors of large symmetric matrices From: Sam Martin - 2007-10-23 15:59:14 Attachments: Message as HTML ```Hi, =20 Anyone familiar with any numerical techniques for finding the eigenvectors of very large but sparse symmetric matrices, or just large dense symmetric matrices? Things like a big covariance matrix, or an undirected graph.=20 =20 Seems like a very large field so if anyone has any pointers on what's particularly worth looking at I'd appreciate it.=20 =20 Cheers, Sam =20 =20 =20 ```
 Re: [Algorithms] finding eigenvectors of large symmetric matrices From: Peter-Pike Sloan - 2007-10-23 18:02:50 Attachments: Message as HTML ```Netlib.org (dense), there are packages for sparse but I'm not familiar with= any of them. If you just want the top eigenvector (or want to peel off the top couple) t= he power method works great: http://www.cs.utk.edu/~dongarra/etemplates/node95.html when it works... Peter-Pike Sloan From: gdalgorithms-list-bounces@... [mailto:gdalgorithms-= list-bounces@...] On Behalf Of Sam Martin Sent: Tuesday, October 23, 2007 8:55 AM To: Game Development Algorithms Subject: [Algorithms] finding eigenvectors of large symmetric matrices Hi, Anyone familiar with any numerical techniques for finding the eigenvectors = of very large but sparse symmetric matrices, or just large dense symmetric = matrices? Things like a big covariance matrix, or an undirected graph. Seems like a very large field so if anyone has any pointers on what's parti= cularly worth looking at I'd appreciate it. Cheers, Sam ```
 Re: [Algorithms] finding eigenvectors of large symmetric matrices From: Michael Walter - 2007-10-23 18:38:19 ```Hi, the QR algorithm should work well (when preprocessing your matrix to upper Hessenberg form, you could use e.g. Givens rotations in order to exploit sparseness of your matrix) and gives the full set of eigenvectors. Regards, Michael On 10/23/07, Sam Martin wrote: > > > > > Hi, > > > > Anyone familiar with any numerical techniques for finding the eigenvectors > of very large but sparse symmetric matrices, or just large dense symmetric > matrices? Things like a big covariance matrix, or an undirected graph. > > > > Seems like a very large field so if anyone has any pointers on what's > particularly worth looking at I'd appreciate it. > > > > Cheers, > > Sam > > > > > > > ------------------------------------------------------------------------- > This SF.net email is sponsored by: Splunk Inc. > Still grepping through log files to find problems? Stop. > Now Search log events and configuration files using AJAX and a browser. > Download your FREE copy of Splunk now >> http://get.splunk.com/ > _______________________________________________ > GDAlgorithms-list mailing list > GDAlgorithms-list@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list > ```
 Re: [Algorithms] finding eigenvectors of large symmetric matrices From: C. Gerald Knizia - 2007-10-30 20:40:58 ```Sam Martin wrote: > Anyone familiar with any numerical techniques for finding the > eigenvectors of very large but sparse symmetric matrices, or just > large dense symmetric matrices? Things like a big covariance matrix, > or an undirected graph. > > Seems like a very large field so if anyone has any pointers on what's > particularly worth looking at I'd appreciate it. If you are looking for the lowest or lowest few eigenvalues/vectors and they are well separated from the rest of the spectrum your best bet is probably the Davidson method. It is a preconditioned iterative method dealing with symmetric problems. Only evaluation of H x (where H is the matrix and x is a trial vector) is needed, so explicit storage of the matrix is not required and it allows for adjustments to the structure of your symmetric problem. This method (and variants of it) drive many of the solvers for extremely large eigenvalue problems in quantum chemistry. -- - C. Gerald Knizia/cgk | #28673212 | this mail was made with intention. ```