Re: Close to singular matrix with Rcond=10^-21
- From: "John D'Errico" <woodchips@xxxxxxxxxxxxxxxx>
- Date: Sun, 10 Jan 2010 13:27:03 +0000 (UTC)
"Ramachandra Kuravi " <krschaitanya@xxxxxxxx> wrote in message <hicjfj$a7p$1@xxxxxxxxxxxxxxxxxx>...
I am trying to solve a linear system of equations AX=B.
I notice that rank of matrix A differs from its size by exactly 2. As I mesh my domain more and more finely I see the same thing happening again (Size(A)-rank(A)=2). As suggested in earlier threads I tried
1)X=A\B. Results blow up.
2)X=pinv(A)*B. Order of magnitude of results is fine but sign is what is erratic.
3)Though det(A) is =10^119 for a 60/60 sized Matrix A, as A gets larger det(A) blows up even more.
4)I checked for repetitive rows and zero rows but found none.
5)I tried LU decomposition for A and then to invert PINV but same thing happens with the sign of the result. {SVD, QR are no different}.
I would be grateful if some one could put some light on this.
Any more information needed to analyze the problem shall be provided.
It is a singular system, or at least a numerically
singular one. They are not uncommon in this
class of problems.
Very often, this may merely reflect an essential
singularity. For example, suppose I consider a
2-d FEM problem under a situation where any
simple translation does not change the stored
energy in the system. In that case, there will be
exactly two unspecified degrees of freedom, and
the rank of your resulting matrix will be N-2,
where N is the number of unknowns! Remember,
if you can freely translate the problem in either
the x or y direction, then there must be two
free parameters in the problem.
(By the way, don't bother to compute det. It
is numerically meaningless here.)
John
.
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- Close to singular matrix with Rcond=10^-21
- From: Ramachandra Kuravi
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