On an Aitken-Steffensen-Newton type method
Abstract We consider an Aitken-Steffensen type method in which the nodes are controlled by Newton and two-step Newton iterations. We…
On computational complexity in solving equations by Steffensen type methods
Abstract AuthorsIon Păvăloiu Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy Keywordsnonlinear equations in R; iterative methods; Steffensen method.…
On a Newton-Steffensen type method
Abstract In this paper we study the convergence of a Newton-Steffensen type method for solving nonlinear equations in R, introduced by…
On a Steffensen-Hermite method of order three
Abstract In this paper we study a third order Steffensen type method obtained by controlling the interpolation nodes in the…
On a Steffensen type method
Abstract We study a general Steffensen type method based on the inverse interpolation Lagrange polynomial of second degree. We show…
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 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…
Publications
Diffusion in Random Fields. Applications to Transport in Groundwater
Book summaryA self-consistent theory of stochastic modeling of groundwater systems is presented. Mathematical theory is illustrated and complemented by numerical methods and simulation codes. doi: http://doi.org/10.1007/978-3-030-15081-5 book on publisher website…
Read More Methods of Newton and Newton-Krylov type
Books, Chebyshev method, Convergence orders, divided differences, eigenvalue/eigenvector problems, history, inexact/perturbed iterations, iterative methods, Krylov methods, linear systems in Rn, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, secant/chord method, successive approximations
Book summaryLocal convergence results on Newton-type methods for nonlinear systems of equations are studied. Solving of large linear systems by Krylov methods (GMRES, GMBACK, MINPERT) are also dealt with, as…
Read More Solutions with a prescribed interval of positivity for differential systems with nonlocal conditions
AbstractBased on fixed point index, the paper develops a theory of existence, localization and multiplicity of solutions to first-order differential systems subject to linear nonlocal conditions. The main features concern…
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