Abstract The high speed of \(x_{k}\rightarrow x^\ast\in{\mathbb R}\) is usually measured using the C-, Q- or R-orders: \begin{equation}\tag{$C$} \lim \frac…

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…

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…

Abstract We consider the numerical approximation of the linear ill-posed problem of unique continuation for the Helmholtz equation. We first review the conditional stability of this problem and then discuss…

Abstract The starting points of the paper are the classic Lototsky–Bernstein operators. We present an integral Durrmeyer-type extension and investigate some approximation properties of this new class. The evaluation of…

AbstractThis paper deals with aa perturbed heavy ball system with vanishing damping that contains a Tikhonov regularization term, in connection to the minimization problem of a convex Fréchet differentiable function.…