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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 differentiate path leading to a solution of the original system, the scalar parameter determining the progress along the path. A pathfollowing 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 this method shares with interior methods in constrained optimization.
Original language  English 

Pages (fromto)  481508 
Number of pages  28 
Journal  Mathematical Programming Series B 
Volume  92 
Issue number  3 
DOIs  
Publication status  Published  1 May 2002 
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Convergence study of methods for solving systems of nonlinear equations
1/05/00 → 31/12/02
Project: Research