From: C. Gerald Knizia <kritiker@gm...>  20071030 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. 