One option for choosing
is to select a hyperplane passing through
that is
orthogonal to the vector
:
 |
(3) |
So, the Newton iteration becomes:
 |
(4) |
 |
(5) |
Then one can prove that the Newton iteration for (2) will converge to a point
on the curve from
provided that the stepsize
is sufficiently small and that the
curve is regular (rank
).
Having found the new point
on the curve we need to compute the tangent vector at
that point:
 |
(6) |
Furthermore the direction along the curve must be preserved:
, so we get the (
)-dimensional appended system
 |
(7) |
Upon solving this system,
must be normalized.