Abstract
We propose a curvilinear search for nonlinear systems of equations
and path-following methods that are very nonlinear with the dominant part in the tangent space.
The curvilinear search is very easy to implement
and should be used with the (Gauss-)Newton method.
At the cost of one function
evaluation the curvature along the search direction can be
reduced. For zero residual nonlinear least squares problems
and nonlinear systems of equations the (Gauss-)Newton method with
the curvilinear search method converges locally with
q-cubic rate.
For general use, well-defined Jacobians are required, which is
the case for nonlinear Tikhonov regularization
as well as for homotopy-continuation methods.
Numerical results for artificial problems and
standard test problems are given.
Key words
Curvilinear search, Nonlinear equations, Nonlinear least squares,
Tikhonov regularization.
The complete report in PostScript.