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# BV_ORTHOG_BLOCK_CHOL

Orthogonalize a set of vectors \(V\) with the Cholesky QR method, that is, compute \(R=\mathrm{chol}(V^*V)\), then obtain the orthogonalized vectors as \(Q=V R^{-1}\).

## Developer Note

This is plain Cholesky QR, which may fail in case of ill-conditioned \(V\). An iterated version such as CholeskyQR2 should be preferred [Yamamoto et al., 2015].

## References

[Yam15]

Y. Yamamoto, Y. Nakatsukasa, Y. Yanagisawa, and T. Fukaya. Roundoff error analysis of the choleskyqr2 algorithm. Electron. Trans. Numer. Anal., 44:306–326, 2015.

## See Also

BV: Basis Vectors, `BVOrthogBlockType`, `BVSetOrthogonalization()`, `BVOrthogonalize()`, `BV_ORTHOG_BLOCK_GS`, `BV_ORTHOG_BLOCK_TSQR`, `BV_ORTHOG_BLOCK_TSQRCHOL`, `BV_ORTHOG_BLOCK_SVQB`

## Level

advanced

## Location

src/sys/classes/bv/interface/bvorthog.c

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