Geodesic
The analytic SVD: on the non-generic points on the path
Electronic transactions on numerical analysis, Tome 37 (2010), pp. 70-86
A new technique for computing the Analytic SVD is proposed. The idea is to follow a branch of just one simple singular value and the corresponding left/right singular vector. Numerical computation may collapse at non-generic points; we will consider the case when the continuation gets stuck due to a nonzero multiple singular value. We interpret such a point as a singularity of the branch. We employ singularity theory in order to describe and classify this point. Since its codimension is one, we meet such a point "rarely."
Classification : 65F15
Keywords: SVD, ASVD, continuation, singularity theory 
@article{ETNA_2010__37__a22,
     author = {Janovsk\'a,  D\'a\v{s}a and Janovsk\'y,  Vladim{\'\i}r},
     title = {The analytic {SVD:} on the non-generic points on the path},
     journal = {Electronic transactions on numerical analysis},
     pages = {70--86},
     year = {2010},
     volume = {37},
     zbl = {1205.65154},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2010__37__a22/}
}
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Janovská,  Dáša; Janovský,  Vladimír. The analytic SVD: on the non-generic points on the path. Electronic transactions on numerical analysis, Tome 37 (2010), pp. 70-86. http://geodesic.mathdoc.fr/item/ETNA_2010__37__a22/