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

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

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

Abstract AuthorsIoannis K. Argyros (Cameron University, USA) Emil Cătinaş (Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy) Ion Păvăloiu (Tiberiu…

Abstract We use perturbed Steffensen-Aitken methods to approximate a locally unique solution of an operator equation in a Banach space. Using…

Abstract We use inexact Steffensen-Aitken-type methods to approximate implicit functions in a Banach space. Using a projection operator our equation reduces to…

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…

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

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

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

Abstract The Ostrowski theorem is a classical result which ensures the attraction of all the successive approximations xk+1 = G(xk) near a fixed…

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

AbstractWe comparatively use some classical spectral collocation methods as well as highly performing Chebfun algorithms in order to compute the eigenpairs of second order singular Sturm-Liouville problems with separated self-adjoint…

Read More AbstractWe are concerned with the study of some classical spectral collocation methods as well as with the new software system Chebfun in computing high order eigenpairs of singular and regular…

Read More AbstractWe solve by Chebyshev spectral collocation some genuinely nonlinear Liouville-Bratu-Gelfand type, 1D and a 2D boundary value problems. The problems are formulated on the square domain [−1, 1] × [−1,…

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