> On 14 Aug 2023, at 10:39 AM, maitri ksh <maitri....@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 > > >
