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Hello,
I continued work on the BDCSVD (bidiagonalizing divide-and-conquer SVD),
building on the excellent work of the group of students at ensimag in
Grenoble. The basic algorithm is now fully implemented. It took me longer
than expected; small mistakes and short-cuts that I took lead to loss of
accuracy. However, at the moment all tests pass, it seems accurate on
random matrices, and it's faster than JacobiSVD (about a factor of four
for a 160-by-160 matrix).
I used the bisection method to solve the nonlinear equation at the heart
of the algorithm, which is hardly state-of-the-art. In fact, I think most
of the lines of code I added can be improved, so I intend to spend some
time optimizing and fine-tuning the BDCSVD class.
Thanks again to Gauthier, Ncolas, Jean and Pierre for their work. Their
well-documented code and their report made it easy for me to get started.
Jitse