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 <[email protected]> escribió: > > > >> On 14 Aug 2023, at 10:39 AM, maitri ksh <[email protected]> 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
