On approximating the eigenvalues and eigenvectors of linear continuous operators

26 Dec 2017

Abstract We consider the computing of an eigenpair (an eigenvector \(v=(v^{(i)})_{i=1,n}\) and an eigenvalue \(\lambda\)) of a matrix \(A\in\mathbb{R}^{n\times n}\), by…

On the Chebyshev method for approximating the eigenvalues of linear operators

25 Dec 2017

Abstract We study the approximation of an eigenpair (an eigenvalue and a corresponding eigenvector) of a a linear operator T from…

A note on inexact secant methods

25 Dec 2017

Abstract The inexact secant method \([x_{k-1},x_{k};F]s_{k}=-F(x_k) +r_k\), \( x_{k+1}=x_k+s_k\), \( k=1,2,\ldots\), \( x_0,x_1 \in {\mathbb R}^n\) for solving the nonlinear system…

On some Steffensen-type iterative methods for a class of nonlinear equations

24 Dec 2017

Abstract Consider the nonlinear equations \(H(x):=F(x)+G(x)=0\), with \(F\) differentiable and \(G\) continuous, where \(F,G,H:X \rightarrow X\) are nonlinear operators and \(X\)…

On some iterative methods for solving nonlinear equations

23 Dec 2017

Abstract Consider the nonlinear equation \(H(x):=F(x)+G(x)=0\), with \(F\) differentiable and \(G\) continuous, where \(F,G,H:X \rightarrow X\), \(X\) a Banach space. The…

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

21 Dec 2017

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

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

21 Dec 2017

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

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

20 Dec 2017

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

Optimal algorithms concerning the solving of equations by interpolation

20 Dec 2017

Abstract In this paper we approach two aspects concerning the optimality problems arising from the consideration of the iterative methods for…

On an Aitken type method

1 Nov 2007

Abstract In this note we study the convergence of a generalized Aitken type method for approximating the solutions of nonlinear…

iterative methods

the solution sought is a limit of a sequence of elements, and each element can be generated based on the previous ones. Initial elements are supposed to be given. Usual iterative methods are the Newton method, the successive approximations, etc.

On approximating the eigenvalues and eigenvectors of linear continuous operators

On the Chebyshev method for approximating the eigenvalues of linear operators

A note on inexact secant methods

On some Steffensen-type iterative methods for a class of nonlinear equations

On some iterative methods for solving nonlinear equations

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

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

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

Optimal algorithms concerning the solving of equations by interpolation

On an Aitken type method

iterative methods

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