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 computational complexity in solving equations by Steffensen type methods

6 years ago

Abstract AuthorsIon Păvăloiu Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy Keywordsnonlinear equations in R; iterative methods; Steffensen method.…

On computational complexity in solving equations by interpolation methods,

6 years ago

Abstract AuthorsIon Păvăloiu (Tiberiu Popoviciu Institute of Numerical Analysis) KeywordsPDFScanned paper: on the journal website. Latex version of the…

On the r-convergence orders of the inexact perturbed Newton methods

6 years ago

Abstract The inexact perturbed Newton methods recently introduced by us are variant of Newton method, which assume that at each step…

Estimating the radius of an attraction ball

6 years ago

Abstract Given a nonlinear mapping \(G:D\subseteq \mathbb{R}^n\rightarrow \mathbb{R}^n\) differentiable at a fixed point \(x^\ast\), the Ostrowski theorem offers the sharp…

On the convergence of some quasi-Newton iterates studied by I. Păvăloiu

6 years ago

Abstract In 1986, I. Păvăloiu [6] has considered a Banach space and the fixed point problem \[x=\lambda D\left( x\right) +y,…

The inexact, inexact perturbed and quasi-Newton methods are equivalent models

6 years ago

Abstract A classical model of Newton iterations which takes into account some error terms is given by the quasi-Newton method,…

Sufficient convergence conditions for certain accelerated successive approximations

6 years ago

Abstract We have recently characterized the q-quadratic convergence of the perturbed successive approximations. For a particular choice of the parameters, these…

Affine invariant conditions for the inexact perturbed Newton method

6 years ago

Abstract The high q-convergence orders of the inexact Newton iterates were characterized by Ypma in terms of some affine invariant…

Inexact perturbed Newton methods and applications to a class of Krylov solvers

6 years ago

Abstract Inexact Newton methods are variant of the Newton method in which each step satisfies only approximately the linear system…

On accelerating the convergence of the successive approximations method

6 years ago

Abstract No q-superlinear convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\) may be attained by the successive approximations when…

solving F(x)=0 iteratively

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