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.

Bilateral approximations of solutions of equations by order three Steffensen-type methods

8 years ago

Abstract We study the convergence of a method of Steffensen-type, which is obtained from the Lagrange polynomial of inverse interpolation with…

Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences

8 years ago

Abstract We study the conditions under which the well-known Aitken-Steffensen method for solving equations leads to monotonic sequences whose terms…

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).…

Solving the equations by interpolation

8 years ago

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

8 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

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

8 years ago

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

8 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

8 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

8 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 \(X\)…

solving F(x)=0 iteratively

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