Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1912-68
Keywords
Rational approximation model, Gauss-Newton method, nonlinear equations, local convergence
First Page
264
Last Page
280
Recommended Citation
WANG, H, & WANG, Q (2021). A new Gauss--Newton-like method for nonlinear equations. Turkish Journal of Mathematics 45 (1): 264-280. https://doi.org/10.3906/mat-1912-68
