Convergence study of methods for solving systems of nonlinear equations

Project: Research

Project Details


The asymptotic convergence of parameterized variants of
Newton's method for the solution of nonlinear systems of
equations is considered in this project.
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 homotopy-type
algorithm, which involves an inner iteration
in which the perturbed systems are approximately solved, is
developed. We show 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.
Effective start/end date1/05/0031/12/02


  • componentwise Q-superlinear convergence.
  • Nonlinear systems of equations
  • homotopy-type method

Research Output

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

Gould, N., Orban, D., Sartenaer, A. & Toint, P., 1 May 2002, In : Mathematical Programming Series B. 92, 3, p. 481-508 28 p.

Research output: Contribution to journalArticle

Open Access
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