The Defect Correction Principle and Discretization Methods.
The Dependence of Critical Parameter Bounds on the Monotonicity of a Newton Sequence.
The effect of rounding errors on a certain class of iterative methods
In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newton-like methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitz-type hypotheses on the mth Fréchet derivative (m ≥ 2 an integer) instead of the first one, we provide sufficient convergence conditions for the inexact Newton-like method that is actually generated on the computer. Moreover,...
The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions.
The finite element method for ill-posed problems
The finite element method for non-linear problems
The fourth order accuracy decomposition scheme for an evolution problem
In the present work, the symmetrized sequential-parallel decomposition method with the fourth order accuracy for the solution of Cauchy abstract problem with an operator under a split form is presented. The fourth order accuracy is reached by introducing a complex coefficient with the positive real part. For the considered scheme, the explicit a priori estimate is obtained.
The fourth order accuracy decomposition scheme for an evolution problem
In the present work, the symmetrized sequential-parallel decomposition method with the fourth order accuracy for the solution of Cauchy abstract problem with an operator under a split form is presented. The fourth order accuracy is reached by introducing a complex coefficient with the positive real part. For the considered scheme, the explicit a priori estimate is obtained.
The instability of some gradient methods for ill-posed problems.
The Metric Gradient in Normed Linear Spaces.
The Newton-kantorovich Method under Mild Differentiability Conditions and the Patak Error Estimates.
The norm convergence of a Magnus expansion method
We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method is investigated.
The perturbed generalized proximal point algorithm
The Perturbed Generalized Tikhonov's Algorithm
We work on the research of a zero of a maximal monotone operator on a real Hilbert space. Following the recent progress made in the context of the proximal point algorithm devoted to this problem, we introduce simultaneously a variable metric and a kind of relaxation in the perturbed Tikhonov’s algorithm studied by P. Tossings. So, we are led to work in the context of the variational convergence theory.
The perturbed Tikhonov's algorithm and some of its applications
The rate of convergence of a modified Newton's process
The Rate of Convergence of Newtons' Process.
The Rothe method and time periodic solutions to the Navier-Stokes equations and equations of magnetohydrodynamics
The existence of a periodic solution of a nonlinear equation is proved. The theory developed may be used to prove the existence of a periodic solution of the variational formulation of the Navier-Stokes equations or the equations of magnetohydrodynamics. The proof of the main existence theorem is based on Rothe method in combination with the Galerkin method, using the Brouwer fixed point theorem.
The Secant Method and Fixed Points of Nonlinear Operators.
The solution existence and convergence analysis for linear and nonlinear differential-operator equations in Banach spaces within the Calogero type projection-algebraic scheme of discrete approximations
The projection-algebraic approach of the Calogero type for discrete approximations of linear and nonlinear differential operator equations in Banach spaces is studied. The solution convergence and realizability properties of the related approximating schemes are analyzed. For the limiting-dense approximating scheme of linear differential operator equations a new convergence theorem is stated. In the case of nonlinear differential operator equations the effective convergence conditions for the approximated...