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Things to follow up #2401:
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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.
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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.
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Posteriori enclosures for ball arithmetic.
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Add a square root-avoiding algorithm (keeping norms factored out) for exact/symbolic fields.
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