Reverse Communication Structure for Shift-Invert

   The reverse communication interface routine for all problem types is __aupd. If the eigenvalue problem (3.2.1) is a double precision non-symmetric one, then the subroutine to use is dnaupd. First the reverse communication loop structure will be described and then the details and nuances of the problem set up will be discussed. We shall use the symbol OP  for the operator that is applied to vectors in the Arnoldi/Lanczos process and will stand for the matrix to use in the weighted inner product described previously. For the shift-invert spectral transformation mode, OP denotes and denotes ${\bf M}$. They will stand for different matrices in each of the various modes.

The basic idea is to set up a loop that repeatedly calls __aupd. On each return, one must either apply OP or to a specified vector or exit the loop depending upon the value returned in the reverse communication parameter ido.