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On the convergence order of some Aitken-Steffensen type methods

8 years ago

Abstract In this note we make a comparative study of the convergence orders for the Steffensen, Aitken and Aitken-Steffensen methods.…

On a third order iterative method for solving polynomial operator equations

8 years ago

Abstract We present a semilocal convergence result for a Newton-type method applied to a polynomial operator equation of degree (2).…

Aitken-Steffensen-type methods for nonsmooth functions (III)

8 years ago

Abstract We provide sufficient conditions for the convergence of the Steffensen method for solving the scalar equation $f(x)=0$, without assuming…

On some Aitken-Steffensen-Halley-type method for approximating the roots of scalar equations

8 years ago

Abstract We extend the Aitken-Steffensen method to the Halley transformation. Under some rather simple assumptions we obtain error bounds for…

Aitken-Steffensen-type methods for nonsmooth functions (II)

8 years ago

Abstract We present some new conditions which assure that the Aitken-Steffensen method yields bilateral approximation for the solution of a…

Aitken-Steffensen-type methods for nondifferentiable functions (I)

8 years ago

Abstract We study the convergence of the Aitken-Steffensen method for solving a scalar equation $f(x)=0$. Under reasonable conditions (without assuming…

On a Halley-Steffensen method for approximating the solutions of scalar equations

8 years ago

Abstract We show that the Steffensen method for solving the scalar equation $f(x)=0$, applied to equation $$h(x)=\frac{f(x)}{\sqrt{f'(x)}}=0,$$ leads to bilateral…

Optimal efficiency index of a class of Hermite iterative methods with two steps

8 years ago

Abstract The inverse interpolatory polynomials of Hermite type with 2 nodes, allhaving the same order of multiplicity $q\in N$, provide…

On the Heron’s method for approximating the cubic root of a real number

8 years ago

Abstract (soon) AuthorsDan Luca Tiberiu Popoviciu Institute of Numerical Analysis Ion Păvăloiu Tiberiu Popoviciu Institute of Numerical Analysis KeywordsPDFScanned paper:…

Observations concerning some approximation methods for the solutions of operator equations

8 years ago

Abstract (soon) AuthorsIon Păvăloiu (Tiberiu Popoviciu Institute of Numerical Analysis) KeywordsPDFScanned paper. PDF-LaTeX version of the paper. Cite this paper…

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