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He studied the iterative methods for solving nonlinear problems (including Newton type methods for nonlinear systems and successive approximations for fixed point problems).
He has obtained results regarding local convergence of iterates, stability to perturbations, estimations of the radius of an attraction ball (for the successive approximations).
A particular approach was the study of Krylov methods (GMRES, GMBACK, MINPERT) when applied as linear solvers at each step.
His recent interest is the study of the convergence orders. The paper http://doi.org/10.1016/j.amc.2018.08.006 he has published in 2019 is the first survey in this field, followed by another survey-type paper, in 2021, published in SIAM Review: http://doi.org/10.1016/j.amc.2018.08.006
In a subsequent paper, has has studied the superlinear convergence, and shown that it can be classified in four classes, with applications to classical optimization methods BFGS, DFP, SR-1. Further results are about to be published.