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# SVDLANCZOS

SVDLANCZOS = “lanczos” - A basic Golub-Kahan-Lanczos bidiagonalization method with explicit restart.

## Notes

Only available for standard SVD problems.

This solver is very basic and is not recommended in general, since it will not be competitive with respect to other solvers.

The implemented method is Lanczos bidiagonalization with explicit restart and deflation. Generally, it is much better to use Lanczos with implicit restart (also known as thick-restart Lanczos) as implemented in `SVDTRLANCZOS`.

The implementation includes a one-sided orthogonalization option, and efficient parallel orthogonalization, see the details in [Hernandez et al., 2007, Hernández et al., 2008].

## References

[Her07c]

V. Hernandez, J. E. Roman, and A. Tomas. Restarted Lanczos bidiagonalization for the SVD in SLEPc. Technical Report STR-8, Universitat Politècnica de València, 2007. URL: https://slepc.upv.es/documentation.

[Her08]

V. Hernández, J. E. Román, and A. Tomás. A robust and efficient parallel SVD solver based on restarted Lanczos bidiagonalization. Electron. Trans. Numer. Anal., 31:68–85, 2008. URL: https://etna.ricam.oeaw.ac.at/volumes/2001-2010/vol31/abstract.php?pages=68-85.

## See Also

SVD: Singular Value Decomposition, Mathematical Background, `SVD`, `SVDType`, `SVDSetType()`, `SVDSetProblemType()`, `SVDTRLANCZOS`

## Level

beginner

## Location

src/svd/impls/lanczos/gklanczos.c

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