Correction

We assume that $X^0$ is close to the curve. To find the point $x_{i+1}$ 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:

\begin{displaymath}
\left\{ \begin{array}{lcl}
F(x) &=& 0, \\
g(x) &=& 0.
\end{array}\right.
\end{displaymath} (2)

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



Subsections