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Correction

We assume that X0 is close to the curve. To find the point xi+1 on the curve we use a Newton-like procedure. Since the standard Newton iterations can only be applied to systems with the same number of equations as unknowns, we have to append an extra scalar condition:

ì
ï
í
ï
î
F(x)
=
0,
g(x)
=
0.
(2)

The question is how to choose the function g(x).



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