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FETI and LDL^T decomposition
In the FETI method, one need the generalized inverse of a sparse matrix K.
In my case, K is a matrix arising from the finite element discretization on a tetrahedral mesh
of linear elasticity equations. I know how to compute the gereralized inverse from the LDL^T but I am not sure how to compute the LDL^T decomposition efficently. The algorithm use both rows and columns of the matrix...
Should I use a left or right looking algorihtm ?
If someone can provide me any hint to do that, I would appreciate a lot.
Thank you !
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Re: L D LT decomposition
I believe LAPACK has an efficient LDLT algorithm. I'm not sure whether it's been implemented for complex-valued matrices but the algorithm should be fairly straightforward to extend to complex numbers. You can find bits of code at:
http://www.alglib.net/matrixops/symmetric/ldlt.php
For sparse systems I'd suggest using SPOOLES rather than LAPACK or writing the algorithm yourself. A parallel implementation also exists.
More generally, a singular value decomposition might be more efficient at finding the pseudo inverse - depending on the structure of your matrix.
-- Biswajit