In this paper a simplified friction problem and iterative second-order algorithms for its solution are analyzed in infinite dimensional function spaces. Motivated from the dual formulation, a primal-dual active set strategy and a semismooth Newton method for a regularized problem as well as an augmented Lagrangian method for the original problem are presented and their close relation is analyze...

Let {Q„)denote a sequenceof quadrature formulas, Q„(j) m Yfj-iW^fix^), such that ß„(/) -> P0 j(x) dx for all / G CTO, 1], Let 0 < e < \ and a sequence (aX_j.be given, where a, ä si ^ a, 5 • • • , and where a„ —> 0 as n —* c°. Then there exists a function / G CTO, l]and a sequence |nt-)"=i suchthat |/(x)| g 2(7,71(1 4e)|, and such that n,Kx)dx Q„k(1) = ak,k = 1,2, 3, ••• .

In this study an unpopular method of quadrature formulas for receiving iterative methods for solving nonlinear equations is applied. It is proved for the presented iterative methods that the order of convergence is equal to two or three. The executed comparative numerical experiments show the efficiency of the presented methods.

In this paper, we propose new variants of Newton’s method based on quadrature formula and power mean for solving nonlinear unconstrained optimization problems. It is proved that the order of convergence of the proposed family is three. Numerical comparisons are made to show the performance of the presented methods. Furthermore, numerical experiments demonstrate that the logarithmic mean Newton’...

In this paper, the numerical solution of nonlinear Fredholm integral equations of second kind is considered by Sinc method. This numerical method combines a discrete Sinc collocation method with the Newton iterative process that involves solving a nonlinear system of equations. We provide an error analysis for the method. So far approximate solutions with polynomial convergence have been report...

We derive a simple accuracy matching strategy for inexact Gauss Newton methods and apply it to the numerical solution of boundary value problems of ordinary differential equations by collocation. The matching strategy is based on an affine contravariant convergence theorem, i.e., the characteristic constants are invariant under affine transformations of the domain. The inexact Gauss Newton meth...

In the present work we have studied superconvergence of Hadamard finite-part integral. We have studied the second-order and the third-order quadrature formulae of Newton-Cotes type. We follow works [Sun, Wu, 2005b], [Lü, Wu, 2005] and work [Wu, Yu and Zhang, 2009] and introduce new rule which gives the same convergence rate as rules in [Lü and Wu, 2005] and [Wu, Yu and Zhang, 2009] but in more ...

We consider the fast solution of large, piecewise smooth minimization problems as typically arising from the nite element discretization of porous media ow. For lack of smoothness, usual Newton multigrid methods cannot be applied. We propose a new approach based on a combination of convex minization with constrained Newton linearization. No regularization is involved. We show global convergence...

Abstract. To find the approximate solutions of a weakly singular integral equation by the collocation method it is necessary to solve linear systems whose coefficients are expressed as integrals. These integrals cannot usually be computed exactly. We get the fully discrete collocation method when we approximate the integrals by quadrature formulas on nonuniform grid. In this paper an appropriat...