2002 Archives | Tiberiu Popoviciu Institute of Numerical Analysis

Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. Part II. Indirect approximation

September 21, 2018

2002

Abstract In this paper, we continue the study initiated in our previous work [3] and design a projection-like algorithm to…

Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. Part I. Direct (variational) approximation

September 21, 2018

Călin-Ioan Gheorghiu

(original), paper

2002

AbstractPublisher Name We consider a nonlinear, second-order, two-point boundary value problem that models some reaction-diffusion precesses. When the reaction term…

On the superlinear convergence of the successive approximations method

February 10, 2018

Emil Cătinaş

(original), fixed point theory, linear systems in Rn, Numerical Analysis, paper

2002

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

Affine invariant conditions for the inexact perturbed Newton method

February 10, 2018

Emil Cătinaş

(original), inexact/perturbed iterations, iterative methods, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, paper

2002

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

On the approximation of solutions to nonlinear operators between metric spaces

January 21, 2018

Ion Păvăloiu

(original), paper

2002

Abstract A Gauss-Seidel method for linear systems, based on decomposing the matrix system into four submatrices blocks, has been proposed…

On a third order iterative method for solving polynomial operator equations

January 20, 2018

Emil Cătinaş

(original), Chebyshev method, eigenvalue/eigenvector problems, iterative methods, nonlinear equations in Banach spaces, Numerical Analysis, paper, semilocal convergence

2002

Abstract We present a semilocal convergence result for a Newton-type method applied to a polynomial operator equation of degree \(2\).…

Aitken-Steffensen-type methods for nonsmooth functions (II)

January 20, 2018

Ion Păvăloiu

(original), paper

2002

Abstract We present some new conditions which assure that the Aitken-Steffensen method yields bilateral approximation for the solution of a…

Aitken-Steffensen-type methods for nonsmooth functions (I)

January 20, 2018

Ion Păvăloiu

(original), paper

2002

Abstract We study the convergence of the Aitken-Steffensen method for solving a scalar equation \(f(x)=0\). Under reasonable conditions (without assuming…