Can Adaption Help on the Average.
Caractérisations de la convergence locale de la méthode des approximations successives
Cases when the use of the analytic method for solving differential equations is better than the use of numerical ones
Common fixed points of a finite family of asymptotically pseudocontractive maps.
Common solutions of an iterative scheme for variational inclusions, equilibrium problems, and fixed point problems.
Comparing the radii of some balls appearing in connection to three local convergence theorems for Newton's method.
Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces.
Comparison theorems for weak splittings of bounded operators.
Computation of derivatives in the finite element method
Computer-assisted proofs for fixed point problems in Sobolev spaces.
Computing the numerical range of Krein space operators
Consider the Hilbert space (H,〈• , •〉) equipped with the indefinite inner product[u,v]=v*J u,u,v∈ H, where J is an indefinite self-adjoint involution acting on H. The Krein space numerical range WJ(T) of an operator T acting on H is the set of all the values attained by the quadratic form [Tu,u], with u ∈H satisfying [u,u]=± 1. We develop, implement and test an alternative algorithm to compute WJ(T) in the finite dimensional case, constructing 2 by 2 matrix compressions of T and their easily determined...
Concerning the convergence of a modified Newton-like method.
Concerning the rate of convergence of Newton's process
Conditions de convergence pour les algorithmes itératifs monotones, autonomes et non déterministes
Cones and error bounds for linear iterations.
Contractivity in the Numerical Solution of Initial Value Problems.
Convergence analysis of a one-step intermediate Newton iterative scheme.
Convergence analysis of finite difference schemes for semi-linear initial-value problems
Convergence comparison of several iteration algorithms for the common fixed point problems.
Convergence conditions for Secant-type methods
We provide new sufficient convergence conditions for the convergence of the secant-type methods to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, and Lipschitz-type and center-Lipschitz-type instead of just Lipschitz-type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than earlier ones and under our convergence hypotheses we can cover cases where earlier conditions...