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From: JuliaLang/LinearAlgebra.jl#203
@mschauer wrote:
It would be nice to have a the semidefinite Cholesky or LDL' decomposition, which allows semidefinite matrices, is more stable and avoids computation of square roots. This makes most sense as generic julia algorithm, because for BLAS floats pivoted Cholesky does the trick. I remember that pivoting was difficult for abstract matrices.
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