Nondiscrete induction and iterative processes

Extended Kantorovich theory for solving nonlinear equations with applications

In this chapter the applicability of inexact two-point Newton-like method for solving nonlinear equations is extended. Moreover, we present some numerical examples validating the theoretical results.

Inexact two-point Newton-like methods

On the complexity of a unified convergence analysis for iterative methods

In this paper, we present a third-order iterative method based on Potra-Pt{a}k method to compute the approximate multiple roots of nonlinear equations. The method requires two evaluations of the function and one evaluation of its first derivative per iteration and it has the efficiency index equal to $3^{\frac{1}{3}}\approx 1.44225$. We describe the analysis of the proposed methods along with numerical experiments including comparison with existing methods. Moreover, the attraction basins are shown and compared with other existing methods.

Nondiscrete induction and iterative processes

Citations

Extended Kantorovich theory for solving nonlinear equations with applications

Inexact two-point Newton-like methods

On the complexity of a unified convergence analysis for iterative methods

Modified Potra-Pt\'ak method to determine the multiple zeros of nonlinear equations

Extended Traub–Woźniakowski convergence and complexity of Newton iteration in Banach space☆

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