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# KSPGMRESClassicalGramSchmidtOrthogonalization

This is the basic orthogonalization routine using classical Gram-Schmidt with possible iterative refinement to improve the stability

## Synopsis

    PetscErrorCode KSPGMRESClassicalGramSchmidtOrthogonalization(KSP ksp, PetscInt it)

Collective, No Fortran Support

## Input Parameters

- ksp - `KSP` object, must be associated with `KSPGMRES`, `KSPFGMRES`, or `KSPLGMRES` Krylov method

- it - one less than the current GMRES restart iteration, i.e. the size of the Krylov space

## Options Database Keys

- -ksp_gmres_classicalgramschmidt (true|false) - Activates `KSPGMRESClassicalGramSchmidtOrthogonalization()`

- -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.

## Note

Use `KSPGMRESSetCGSRefinementType()` to determine if iterative refinement is to be used. This is much faster than `KSPGMRESModifiedGramSchmidtOrthogonalization()` but has the small possibility of stability issues that can usually be handled by using a single step of iterative refinement with `KSPGMRESSetCGSRefinementType()`

## See Also

KSP: Linear System Solvers, `KSPGMRESCGSRefinementType`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESSetCGSRefinementType()`, `KSPGMRESGetCGSRefinementType()`, `KSPGMRESGetOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`

## Level

intermediate

## Location

src/ksp/ksp/impls/gmres/borthog2.c

## Examples

src/ksp/ksp/tutorials/ex5f.F90

Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages