solving F(x)=0 iteratively

The solution of the nonlinear equation/system of equations F(x)=0 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 secant method, etc.

On the Steffensen method for solving nonlinear operator equations

6 years ago

Abstract We consider the equation \[F\left( x\right) =x-A\left( x\right)=0,\] where \(A\) is an operator from a Banach space \(X\) to…

On approximating the eigenvalues and eigenvectors of linear continuous operators

6 years ago

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

6 years ago

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

6 years ago

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

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

6 years ago

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

6 years ago

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)

6 years ago

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)

6 years ago

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

6 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…

Optimal algorithms concerning the solving of equations by interpolation

6 years ago

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

solving F(x)=0 iteratively

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