Re: strange linear system
- From: Helmut Jarausch <jarausch@xxxxxxxxxxxxxxxxxxx>
- Date: Fri, 26 Jan 2007 11:25:56 +0100
asdf 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?
In a similar case it was helpful to look at the left(!) singular vector
corresponding to that 0 singular value. Given
V S U' = A, the singular values (on the diagonal of S) are sorted w.r.t
decreasing value. Setting v0:= V(:,8000), one has
v0'*A = 0, i.e. v0 gives exactly that linear combination of equations
which is redundant.
Probably the same problem occurs with smaller parameters giving a much
smaller matrix showing the same redundancy.
If that doesn't give enough insight, compute the right singular vector
u0:= U(:,8000) which spans the nullspace of A, hinting at a superfluous
unknown.
--
Helmut Jarausch
Lehrstuhl fuer Numerische Mathematik
RWTH - Aachen University
D 52056 Aachen, Germany
.
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- From: asdf
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