
The Riemannian SVD
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3.10 NON-SYMMETRIC CONTINUOUS-TIME POWER METHOD FOR THE SMALL-
EST SINGULAR VALUE
We can exploit these insights to calculate the smallest singular triplet of a matrix A 6 i~p•
as follows. Consider the 'asymmetric' continuous-time power method:
= - ~ (16)
i) A T -~Iq v v '
with
= ~(ur~-
v rv) I
(~r~ + ~rv) "
Here c~ is a user-defined real scalar. When it is chosen such that a > amin(A), u and v will
converge to the left resp. right singular vector corresponding to the smallest singular value
of A. This can be understood by realizing that the 2q (we assume that ...