Sciweavers

Share
MP
2002

Componentwise fast convergence in the solution of full-rank systems of nonlinear equations

11 years 9 months ago
Componentwise fast convergence in the solution of full-rank systems of nonlinear equations
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 Qsuperlinear rate may be attained, both in the direct error and in the residuals, 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 t...
Nicholas I. M. Gould, Dominique Orban, Annick Sart
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 2002
Where MP
Authors Nicholas I. M. Gould, Dominique Orban, Annick Sartenaer, Philippe L. Toint
Comments (0)
books