[petsc-users] eigenvalue problem involving inverse of a matrix

[maitri ksh]

got it, thanks Pierre & Jose.

On Mon, Aug 14, 2023 at 12:50 PM Jose E. Roman <jroman at dsic.upv.es> wrote:

> See for instance ex3.c and ex9.c
> https://slepc.upv.es/documentation/current/src/eps/tutorials/index.html
>
> Jose
>
>
> > El 14 ago 2023, a las 10:45, Pierre Jolivet <pierre.jolivet at lip6.fr>
> escribió:
> >
> >
> >
> >> On 14 Aug 2023, at 10:39 AM, maitri ksh <maitri.ksh at gmail.com> wrote:
> >>
> >> 
> >> Hi,
> >> I need to solve an eigenvalue problem  Ax=lmbda*x, where
> A=(B^-H)*Q*B^-1 is a hermitian matrix, 'B^-H' refers to the hermitian of
> the inverse of the matrix B. Theoretically it would take around 1.8TB to
> explicitly compute the matrix B^-1 . A feasible way to solve this
> eigenvalue problem would be to use the LU factors of the B matrix instead.
> So the problem looks something like this:
> >>                      (((LU)^-H)*Q*(LU)^-1)*x = lmbda*x
> >> For a guess value of the (normalised) eigen-vector 'x',
> >> 1) one would require to solve two linear equations to get 'Ax',
> >>         (LU)*y=x,             solve for 'y',
> >>        ((LU)^H)*z=Q*y,   solve for 'z'
> >>     then one can follow the conventional power-iteration procedure
> >> 2) update eigenvector: x= z/||z||
> >> 3) get eigenvalue using the Rayleigh quotient
> >> 4) go to step-1 and loop through with a conditional break.
> >>
> >> Is there any example in petsc that does not require explicit
> declaration of the matrix 'A' (Ax=lmbda*x) and instead takes a vector 'Ax'
> as input for an iterative algorithm (like the one above). I looked into
> some of the examples of eigenvalue problems ( it's highly possible that I
> might have overlooked, I am new to petsc) but I couldn't find a way to
> circumvent the explicit declaration of matrix A.
> >
> > You could use SLEPc with a MatShell, that’s the very purpose of this
> MatType.
> >
> > Thanks,
> > Pierre
> >
> >> Maitri
>
>
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