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 Limit Periodic Continued Fractions Under Asymptotic Side Conditions.
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...