Turkish Journal of Mathematics
DOI
10.3906/mat-1912-68
Abstract
In this paper, a new Gauss-Newton-like method that is based on a rational approximation model with linear numerator is proposed for solving nonlinear equations. The new method revises the $J_k^\mathrm{T}J_k$ matrix by a rank-one matrix at each iteration. Furthermore, we design a new iterative algorithm for nonlinear equations and prove that it is locally q-quadratically convergent. The numerical results show that the new proposed method has better performance than the classical Gauss-Newton method.
Keywords
Rational approximation model, Gauss-Newton method, nonlinear equations, local convergence
First Page
264
Last Page
280
Recommended Citation
WANG, HAIJUN and WANG, QI
(2021)
"A new Gauss--Newton-like method for nonlinear equations,"
Turkish Journal of Mathematics: Vol. 45:
No.
1, Article 16.
https://doi.org/10.3906/mat-1912-68
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss1/16
