Options Database Key#
-the number of stored vectors to orthogonalize against
The GCR Krylov method supports non-symmetric matrices and permits the use of a preconditioner which may vary from one iteration to the next.
Users can define a method to vary the
preconditioner between iterates via
Restarts are solves with x0 not equal to zero. When a restart occurs, the initial starting solution is given by the current estimate for x which was obtained by the last restart iterations of the GCR algorithm.
KSPFGMRES, when using GCR, the solution and residual vector can be directly accessed at any iterate,
with zero computational cost, via a call to
This implementation of GCR will only apply the stopping condition test whenever ksp->its > ksp->chknorm,
where ksp->chknorm is specified via the command line argument -ksp_check_norm_iteration or via
KSPSetCheckNormIteration(). Hence the residual norm reported by the monitor and stored
in the residual history will be listed as 0.0 before this iteration. It is actually not 0.0; just not calculated.
The method implemented requires the storage of 2 x restart + 1 vectors, twice as much as
Support only for right preconditioning.
S.C. Eisenstat, H.C. Elman, and M.H. Schultz. Variational iterative methods for nonsymmetric systems of linear equations. SIAM Journal on Numerical Analysis, 20(2):345–357, 1983.