petsc-3.10.5 2019-03-28
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# KSPGMRES

Implements the Generalized Minimal Residual method. (Saad and Schultz, 1986) with restart

### Options Database Keys

| -ksp_gmres_restart <restart> | - the number of Krylov directions to orthogonalize against
| -ksp_gmres_haptol <tol> | - sets the tolerance for "happy ending" (exact convergence)
| -ksp_gmres_preallocate | - preallocate all the Krylov search directions initially (otherwise groups of vectors are allocated as needed)
| -ksp_gmres_classicalgramschmidt | - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
| -ksp_gmres_modifiedgramschmidt | - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
| -ksp_gmres_cgs_refinement_type <never,ifneeded,always> | - determine if iterative refinement is used to increase the stability of the classical Gram-Schmidt orthogonalization.
| -ksp_gmres_krylov_monitor | - plot the Krylov space generated

### Notes

Left and right preconditioning are supported, but not symmetric preconditioning.

### References

1. -YOUCEF SAAD AND MARTIN H. SCHULTZ, GMRES: A GENERALIZED MINIMAL RESIDUAL ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS. SIAM J. ScI. STAT. COMPUT. Vo|. 7, No. 3, July 1986.

### See Also

KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(), KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()

### Level

beginner

### Location

src/ksp/ksp/impls/gmres/gmres.c

### Examples

src/ksp/ksp/examples/tutorials/ex7.c.html
src/ksp/ksp/examples/tutorials/ex8.c.html
src/ksp/ksp/examples/tutorials/ex62.c.html
src/tao/pde_constrained/examples/tutorials/hyperbolic.c.html
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages