Numerical Analysis

Solving the equations by interpolation

About this bookSummary of the book… (to be completed) CoverAuthorIon Păvăloiu Tiberiu Popoviciu Institute of Numerical Analysis TitleOriginal title (in…

On the Steffensen method for solving nonlinear operator equations

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

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 monotonicity of the sequences of approximations obtained by Steffensen’s method

Abstract ? AuthorIon Păvăloiu (Tiberiu Popoviciu Institute of Numerical Analysis) Keywords? PDFScanned paper. PDF-LaTeX version of the paper. Cite this paper…

On the Chebyshev method for approximating the eigenvalues of linear operators

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

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

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

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)

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)

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