ePubs

The open archive for STFC research publications

Full Record Details

Persistent URL http://purl.org/net/epubs/work/40519
Record Status Checked
Record Id 40519
Title Componentwise fast convergence in the solution of full-rank systems of nonlinear equations.
Contributors
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 homotopy-type 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.
Organisation CCLRC , CSE , CSE-NAG
Keywords
Funding Information
Related Research Object(s):
Language English (EN)
Type Details URI(s) Local file(s) Year
Journal Article Math Program B, no. 92 (2002): 481-508. 2002
Showing record 1 of 1
RCUK
Science and Technology Facilities Council Switchboard: 01793 442000