Skip to main content
`Ctrl`+`K`

# BV_ORTHOG_REFINE_IFNEEDED

In the orthogonalization of vectors, do iterative refinement only if a certain criterion is satisfied.

## Note

This is the default. One step of iterative refinement will be done if a certain numerical criterion holds. In ill-conditioned cases, a third orthogonalization can also be done. The criterion is similar to the one proposed in [Daniel et al., 1976]. The parameter \(\eta\) for the criterion can be set in `BVSetOrthogonalization()`.

## References

[Dan76]

J. W. Daniel, W. B. Gragg, L. Kaufman, and G. W. Stewart. Reorthogonalization and stable algorithms for updating the Gram–Schmidt QR factorization. Math. Comp., 30(136):772–795, 1976. doi:10.1090/S0025-5718-1976-0431641-8.

## See Also

BV: Basis Vectors, `BVOrthogRefineType`, `BVSetOrthogonalization()`, `BV_ORTHOG_REFINE_NEVER`, `BV_ORTHOG_REFINE_ALWAYS`

## Level

advanced

## Location

include/slepcbv.h

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