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# KSPGCR
Implements the preconditioned flexible Generalized Conjugate Residual method. [](sec_flexibleksp), 
## Options Database Key

- ***-ksp_gcr_restart <restart> -*** the number of stored vectors to orthogonalize against





## Notes
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 can define a method to vary the
preconditioner between iterates via `KSPGCRSetModifyPC()`.

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.

Unlike `KSPGMRES` and `KSPFGMRES`, when using GCR, the solution and residual vector can be directly accessed at any iterate,
with zero computational cost, via a call to `KSPBuildSolution()` and `KSPBuildResidual()` respectively.

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
the function `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 `KSPGMRES`.
Support only for right preconditioning.


## Contributed by
Dave May


## References

- **** -*** S. C. Eisenstat, H. C. Elman, and H. C. Schultz. Variational iterative methods for
nonsymmetric systems of linear equations. SIAM J. Numer. Anal., 20, 1983



## See Also
 [](ch_ksp), [](sec_flexibleksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPGCRSetRestart()`, `KSPGCRGetRestart()`,
`KSPGCRSetRestart()`, `KSPGCRSetModifyPC()`, `KSPGMRES`, `KSPFGMRES`

## Level
beginner

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/impls/gcr/gcr.c.html#KSPGCR">src/ksp/ksp/impls/gcr/gcr.c</A>

## Examples
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/dm/impls/stag/tutorials/ex4.c.html">src/dm/impls/stag/tutorials/ex4.c</A><BR>


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


[Index of all KSP routines](index.md)  
[Table of Contents for all manual pages](/manualpages/index.md)  
[Index of all manual pages](/manualpages/singleindex.md)