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Nonlinear least-squares (NLS) problems find extensive applications across various fields within the applied sciences.Conventional methods for solving NLS problems often face challenges related to computational efficiency and memory requirements, especially when dealing with large-scale systems.In this paper, the solution to the minimization of nonlinear least squares problems has been obtained using a proposed structured accelerated three-term conjugate gradient method, in which from Taylor series approximations of the objective function's Hessian, the structured vector approximation involving a vector's action on a matrix is obtained.This ensures the satisfaction of a quasi-Newton condition.The technique then employs the structured vector approximation to incorporate additional information from the Hessian of the goal function into the standardized search direction.The proposed method's search direction fulfills the necessary descent criterion.Additionally, numerical tests performed on various test problems show that the suggested approach is remarkably efficient, surpassing some existing competitors.
Yunus et al. (Tue,) studied this question.