Re: strange linear system

In article <1169677690.580088.260150@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
asdf <likemursili@xxxxxxxxx> wrote:
Hi, guys, I encountered a strange problem, say, AX=B, where A is
8000-by-8000 matrix, and the largest singular value is around 0.6, the
least singular value is around 1e-18, and the second least singular
value is around 1e-4.

I tried to use SVD to solve this linear system, zeroing the reciprocal
of the least singular value, however, the result is still not correct.

What's the possible reason? And Is there any method better than SVD in
this case?

The least singular value is essentially 0, meaning the matrix is not
invertible. Therefore for most values of B there will be no X that
solves AX=B. What you get using SVD to "solve" the system is a
least-squares best fit to a solution: a solution to AX=C where C is
as close as possible to B, but not a solution to AX=B.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

Relevant Pages