Re: [eigen] Symmetric Indefinite Solver Support

[Christoph Hertzberg <chtz@xxxxxxxxxxxxxxxxxxxxxxxx>]

On 25.07.2013 00:44, Cowing-Zitron, Christopher wrote:
> I've been going through the Eigen documentation, and it appears that
> all the symmetry-preserving factorizations available require the
> matrix to be positive definite. Obviously, this is necessarily the

SelfAdjointEigenSolver also works on indefinite matrices (of course 
that's a bad choice, if you basically want to solve a linear system).

> case for the built-in LLt and LDLt factorizations, as they don't do
> any pivoting.

LDLt does pivoting (but only 1x1) and it only requires the matrix to be 
semidefinite (positive or negative). It also works for some indefinite 
matrices (those that don't require 2x2 pivoting, e.g. [1 0; 0 -1] is no 
problem).

> But the documentation also claims that the Pardiso and
> Pastix LDLt modules only support definite matrices, whereas I know
> both of those libraries do support 2x2 pivoting for indefinite
> problems. Is this simply an error in the Eigen documentation? Or have

It's certainly possible that there is an error in the documentation.
Did you try out what happens when you pass an indefinite matrix to 
Pardiso/Pastix?


cheers,
Christoph



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Dipl.-Inf., Dipl.-Math. Christoph Hertzberg
Cartesium 0.049
Universität Bremen
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