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math.NA2015
Generalized Kantorovich-type theorem for the Fixed Slope Iterations
Andrei Dubin
The extended modification of the Newton method is considered when the inverse of the derivative (of the operator F(x) in the equation F(x)=0) is replaced by an invertible bounded x…
math.NA2015
An improved convergence theorem for the Newton method under relaxed continuity assumptions
Andrei Dubin
In the framework of the majorization technique, an improved condition is proposed for the semilocal convergence of the Newton method under the mild assumption that the derivative o…