Geodesic
Numerical methods for the computation of analytic singular value decompositions
Electronic transactions on numerical analysis, Tome 1 (1993), pp. 72-88
An analytic singular value decomposition (ASVD) of a path of matrices $E(t)$ is an analytic path of factorizations $E(t) = X(t)S(t)$Y (t)T where $X(t)$ and Y (t) are orthogonal and $S(t)$ is diagonal. The diagonal entries of $S(t)$ are allowed to be either positive or negative and to appear in any order. For an analytic path matrix $E(t)$ an ASVD exists, but this ASVD is not unique.
Classification : 65F25
Keywords: analytic singular value decomposition, singular value decomposition 
@article{ETNA_1993__1__a2,
     author = {Mehrmann,  Volker and Rath,  Werner},
     title = {Numerical methods for the computation of analytic singular value decompositions},
     journal = {Electronic transactions on numerical analysis},
     pages = {72--88},
     year = {1993},
     volume = {1},
     zbl = {0809.65034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1993__1__a2/}
}
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Mehrmann,  Volker; Rath,  Werner. Numerical methods for the computation of analytic singular value decompositions. Electronic transactions on numerical analysis, Tome 1 (1993), pp. 72-88. http://geodesic.mathdoc.fr/item/ETNA_1993__1__a2/