Componentwise fast convergence in the solution of full-rank systems of nonlinear equations
by
Dominique Orban
CERFACS--Parallel Algorithms Project
Coauthors: N.I.M. Gould (Rutherford Appleton Laboratory, UK), A. Sartenaer (Facultés Universitaires Notre-Dame de la Paix, Namur), Ph.L. Toint (Facultés Universitaires Notre-Dame de la Paix, Namur)

The asymptotic convergence of parameterized variants of Newton's method for the solution of nonlinear systems of equations is considered. The original system is perturbed by a term involving the variables and a scalar parameter which is driven to zero as the iteration proceeds. The exact local solutions to the perturbed systems then form a differentiable path leading to a solution of the original system, the scalar parameter determining the progress along the path. A path-following algorithm, which involves an inner iteration in which the perturbed systems are approximately solved, is outlined. It is shown that asymptotically, a single linear system is solved per update of the scalar parameter. It turns out that a componentwise Q-superlinear rate may be attained under standard assumptions, and that this rate may be made arbitrarily close to quadratic. Numerical experiments illustrate the results and we discuss the relationships that this method shares with interior methods in constrained optimization.

Dominique Orban: Reports and publications

Date received: April 30, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahh-14.