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QR factorization enhancements #2402

@fredrik-johansson

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@fredrik-johansson

Things to follow up #2401:

  • Add the Householder algorithm, which is generally considered superior to Gram-Schmidt, especially for ill-conditioned matrices. I'm not sure if there is a big difference in arbitrary-precision arithmetic, but it's worth having both algorithms to compare.

  • Handle complex numbers the expected way, i.e. generating unitary matrices (requires adding _gr_vec_dot_conj and some other helper functions to do cleanly).

  • Currently only full rank matrices are allowed. Either generalize the current implementation, or add separate rank-revealing functions.

  • Posteriori enclosures for ball arithmetic.

  • Add a square root-avoiding algorithm (keeping norms factored out) for exact/symbolic fields.

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