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"
Darstellung und Entwicklung des Restgliedes der Gregoriyschen Quadraturformel mit Hilfe von Spline-Funktionen.
Decompositional analysis of Kronecker structured Markov chains.
Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations
We present two defect correction schemes to accelerate the Petrov-Galerkin finite element methods [19] for nonlinear Volterra integro-differential equations. Using asymptotic expansions of the errors, we show that the defect correction schemes can yield higher order approximations to either the exact solution or its derivative. One of these schemes even does not impose any extra regularity requirement on the exact solution. As by-products, all of these higher order numerical methods can also be...
Deferred Corrections Using Uncentered End Formulas.
Die Determinantenmethode zur Berechnung des charakteristischen Exponenten der endlichen Hillschen Differentialgleichung.
Discrete Newton Methods and Iterated Defect Corrections.
Efficient representations of Green’s functions for some elliptic equations with piecewise-constant coefficients
Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range of...
Efficient Stable Ways to Calculate Continued Fraction Coefficients From some Series.
Ein Verfahren höherer Konvergenzordnung zur Berechnung des charakteristischen Exponenten der Mathieuschen Differentialgleichung.
Eine kurze Anmerkung zur Romberg-Integration.
Encadrement de la fonction sommatoire des inverses des termes d'une progression arithmétique
Ergodic Computations with Continued Fractions and Jacobi's Algorithm.
Estimating the sequence of real binomial coefficients.
Etudes sur les e- et g-algorithmes.
Evaluation of coefficients of a double Chebyshev series of the function g(p(x+y))
Explicit expressions for the coordinates of foci and vertices of a quadric in dependence on the coefficients of its Cartesian equations