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Newton method, invented by physicist Isaac Newton about 300 years ago, is an algorithm that still plays an important role in a wide range of fields, including logistics, financial engineering, ...

SIAM Journal on Numerical Analysis, Vol. 47, No. 3 (2009), pp. 1827-1846 (20 pages) We study the convergence of regularized Newton methods applied to nonlinear operator equations in Hilbert spaces if ...

In general, when a quasi-Newton method is applied to solve a system of nonlinear equations, the quasi-Newton direction is not necessarily a descent direction for the norm function. In this paper, we ...