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From: Alain on 23 Mar 2010 12:34
Hello,

I am computing the 50 first eigenvalues of large matrices (about 140,000 x 140,000) that are symmetric and definite positive (mass M and stiffness K matrices obtained with finite element method).

[z,w]=eigs(K,M,50,'sm');

Something surprises me with the results. While the eigenvalues seem correct (compared to finite element reference code), the eigenvectors are not M-orthonormal, meaning

z'.M.z is NOT equal to identity matrix.

I studied smaller structures (70,000 x 70,000) and I do find that

z'.M.z equals identity

Is there a way to force z to be M-orthonormal or at least M-orthogonal ?

Thanks.

Alain
From: Etienne Balmes on 24 Mar 2010 03:22
The eigs modes are mass orthogonal but not normalized. You can look up the eigs packaging in OpenFEM fe_eig function (solver 6 is a call to eigs)

http://support.sdtools.com/gf/project/openfem/scmsvn/?action=browse&path=%2Ftrunk%2F

this returns mass normalized modeshapes as expected in FEM analysis.
From: Bruno Luong on 24 Mar 2010 04:12
"Etienne Balmes" <balmes.nospam(a)sdtools.com.nospam> wrote in message <hocejh$1bv$1(a)fred.mathworks.com>...
> The eigs modes are mass orthogonal but not normalized. You can look up the eigs packaging in OpenFEM fe_eig function (solver 6 is a call to eigs)
>

It seems OP check correctly "mass-orthogonal". I'm afraid it is the lost of orthogonality in Arnoldi/Lanczos iteration that has been observed.

Bruno
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