Re: Eigenvalues and eigenvectors of an ill-conditioned matrix

jcooper_at_ucalgary.ca
Date: 12/31/04 

Date: 31 Dec 2004 13:44:54 -0800

Some more information might also be helpful here... The
ill-conditioned matrix in question arises from the product A^T A for
another matrix 'A'. 'A' (whose nonzero elements also span many orders
of magnitude) is, in turn, the weighted sum of a set of matrices which
are very nice, but with weights which are the source of the
order-of-magnitude differences.

I expect that the fact that A is a weighted sum will not be
particularly helpful. However, is there a method available for
obtaining the orthogonal matrix which orthogonalizes A without
calculating A^T A as an intermediate (and then calculating the
eigenvectors)?