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# KSPLGMRES
Augments the standard GMRES approximation space with approximations to the error from previous restart cycles. 
## Options Database Keys

- ***-ksp_gmres_restart <restart> -*** total approximation space size (Krylov directions + error approximations)
- ***-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 <refine_never,refine_ifneeded,refine_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
- ***-ksp_lgmres_augment <k> -*** number of error approximations to augment the Krylov space with
- ***-ksp_lgmres_constant -*** use a constant approx. space size (only affects restart cycles < num. error approx.(k), i.e. the first k restarts)



## To run LGMRES(m, k) as described in [1], use
-ksp_gmres_restart <m+k>
-ksp_lgmres_augment <k>




## Note
Supports both left and right preconditioning, but not symmetric.


## Developer Note
This object is subclassed off of `KSPGMRES`


## Contributed by
Allison Baker


## References

- ***[1] -*** A. H. Baker, E.R. Jessup, and T.A. Manteuffel. A technique for accelerating the convergence of restarted GMRES. SIAM Journal on Matrix Analysis and Applications, 26 (2005).



## See Also
 [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPFGMRES`, `KSPGMRES`,
`KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESGetOrthogonalization()`,
`KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`,
`KSPGMRESCGSRefinementType`, `KSPGMRESSetCGSRefinementType()`, `KSPGMRESGetCGSRefinementType()`, `KSPGMRESMonitorKrylov()`, `KSPLGMRESSetAugDim()`,
`KSPGMRESSetConstant()`

## Level
beginner

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/impls/gmres/lgmres/lgmres.c.html#KSPLGMRES">src/ksp/ksp/impls/gmres/lgmres/lgmres.c</A>


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[Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/ksp/ksp/impls/gmres/lgmres/lgmres.c)


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