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# KSPCR
This code implements the (preconditioned) conjugate residuals method 


## Notes
The operator and the preconditioner must be symmetric for this method.

The preconditioner must be POSITIVE-DEFINITE and the operator POSITIVE-SEMIDEFINITE.

Support only for left preconditioning.


## References

- **** -*** Magnus R. Hestenes and Eduard Stiefel, Methods of Conjugate Gradients for Solving Linear Systems,
Journal of Research of the National Bureau of Standards Vol. 49, No. 6, December 1952 Research Paper 2379



## See Also
 [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPCG`

## Level
beginner

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


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