Paper Info
Title
Componentwise fast convergence in the solution of full-rank systems of nonlinear equations
Abstract
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, 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 this method shares with interior methods in constrained optimization.
Year
DOI
Venue
2002
10.1007/s101070100287
Math. Program.
Keywords
Field
DocType
Key words: nonlinear systems of equations – path-following methods – componentwise Q-superlinear convergence,Mathematics Subject Classification (1991): 65K05,90C26,90C51
Rank (linear algebra),Mathematical optimization,Nonlinear system,Linear system,Mathematical analysis,Scalar (physics),Numerical analysis,Predictor–corrector method,Mathematics,Constrained optimization,Newton's method
Journal
Volume
Issue
ISSN
92
3
0025-5610
Citations 
PageRank 
References 
6
0.90
8
Authors
4
Name
Order
Citations
PageRank
Nicholas I. M. Gould11445123.86
Dominique Orban257754.97
Annick Sartenaer316518.66
Philippe L. Toint41397127.90