[petsc-users] SLEPc: smallest eigenvalues

Varun Hiremath varunhiremath at gmail.com
Thu Jul 1 04:37:34 CDT 2021

Hi All,

I am trying to compute the smallest eigenvalues of a generalized system
A*x= lambda*B*x. I don't explicitly know the matrix A (so I am using a
shell matrix with a custom matmult function) however, the matrix B is
explicitly known so I compute inv(B)*A within the shell matrix and solve
inv(B)*A*x = lambda*x.

To compute the smallest eigenvalues it is recommended to solve the inverted
system, but since matrix A is not explicitly known I can't invert the
system. Moreover, the size of the system can be really big, and with the
default Krylov solver, it is extremely slow. So is there a better way for
me to compute the smallest eigenvalues of this system?

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