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Expanding the applicability of Newton’s method and of a robust modified Newton’s method
Applicationes Mathematicae, 2021Summary: Newton's method cannot be used to approximate a solution of a nonlinear equation when the derivative of the function is singular or almost singular. To overcome this problem a modified Newton's method may be used. The Newton-Kantorovich theorem is used to show its convergence. The convergence domain of this method is small in general.
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