Cauchy problems with periodic controls.
Chebyshev polynomials and some methods of approximation.
Composite Sequence Transformations.
Conditions d'application et de convergence de procédés d'extrapolation.
Contraction Properties of Sequence Transformations.
Convergence acceleration by the -algorithm
A new algorithm which generalizes the E-algorithm is presented. It is called the -algorithm. Some results on convergence acceleration for the -algorithm are proved. Some applications are given.
Convergence acceleration of alternating series.
Convergence Acceleration of Limit Periodic Continued Fractions Under Asymptotic Side Conditions.
Convergence Acceleration of Some Sequences by the e-Algorithm.
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...
Converging self-consistent field equations in quantum chemistry – recent achievements and remaining challenges
This paper reviews popular acceleration techniques to converge the non-linear self-consistent field equations appearing in quantum chemistry calculations with localized basis sets. The different methodologies, as well as their advantages and limitations are discussed within the same framework. Several illustrative examples of calculations are presented. This paper attempts to describe recent achievements and remaining challenges in this field.
Corrigendum to the paper "Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory"