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.
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Oliveira et al. (2024) studied this question.
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