A new truncated-perturbed Gauss–Newton method for underdetermined nonlinear least squares problems

Abstract

In this paper, we study the solvability of a truncated-perturbed Gauss–Newton method for solving underdetermined nonlinear least squares problems. Our aim is to address a new analysis of a semilocal convergence to the aforementioned method. In particular, the main theorem is established under a kind of Hölder-relaxed condition, and two special cases of this are obtained. Furthermore, the computational behavior of the considered method is illustrated with some numerical tests.

Keywords:

• Truncated-perturbed Gauss–Newton method
• nonlinear least squares problems
• Hölder-relaxed condition
• semilocal convergence

2020 Mathematics Subject Classifications:

• 65K05
• 49M15
• 49M37

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The third author was supported in part by CNPq [grant number 401864/2022-7] and [grant number 306593/2022-0].