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On some interpolatory iterative methods for the second degree polynomial operators (I)

8 years ago

Abstract In this note we consider the chord (secant) method and the Steffensen method for solving polynomial operators of degree…

On an approximation formula

8 years ago

Abstract We generalize an approximation formula which in some particular cases has been studied by [J.F. Traub 1964] and \…

On some interpolatory iterative methods for the second degree polynomial operators (II)

8 years ago

Abstract In this paper we apply some iterative methods obtained by inverse interpolation, in order to solve some specific classes…

Monotone sequences for approximating the solutions of equations

8 years ago

Abstract We study the local convergence of a Aitken-Steffensen type method for approximating the solutions of nonlinear scalar equations. We…

On the convergence order of the iterative methods

8 years ago

Abstract We study the connection between the convergence order of two sequences. We show that the exist sequences that do…

Remarks on some Newton and Chebyshev-type methods for approximation eigenvalues and eigenvectors of matrices

8 years ago

Abstract We consider a square matrix \(A\) with real or complex elements. We denote \(\mathbb{K}=\mathbb{R}\) or \(\mathbb{C}\) and we are…

On a generalization of the Steffensen method

8 years ago

Abstract We extend the Steffensen method for solving the equation \(f\left( x\right)=0\) to the setting of the Banach spaces, \(f:X\rightarrow…

Remarks on the secant method for the solution of nonlinear operator equations

8 years ago

Abstract Let \(X_{1},X_{2}\) be two Banach spaces and \(f:X_{1}\rightarrow X_{2}\) a nonlinear equation. We study the chord method for solving…

On the convergency of a Steffensen-type method

8 years ago

Abstract Let \(X_{1},X_{2}\) be two Banach spaces, \(f:X_{1}\rightarrow X_{2}\) a nonlinear mapping. We study the convergence of the Steffensen method for…

On the chord method

8 years ago

Abstract Let \(X_{1},X_{2}\) be two Banach spaces, \(f:X_{1}\rightarrow X_{2}\) a nonlinear mapping and consider the chord method for solving the…

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