Ein verallgemeinerter Kettenbruch-Algorithmus zur rationalen Hermite-Interpolation.
Equiconvergence of some sequences of rational functions.
Error autocorrection in rational approximation and interval estimates. [A survey of results.]
The error autocorrection effect means that in a calculation all the intermediate errors compensate each other, so the final result is much more accurate than the intermediate results. In this case standard interval estimates (in the framework of interval analysis including the so-called a posteriori interval analysis of Yu. Matijasevich) are too pessimistic. We shall discuss a very strong form of the effect which appears in rational approximations to functions. The error autocorrection effect occurs...
Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals.
Evaluation of the Fermi-Dirac integral of half-integer order
Formes linéaires invariantes par translation et approximation rationnelle
General Order Newton-Padé Approximants for Multivariate Functions.
Geometric Convergence of Rational Approximations to e-z in Infinite Sectors.
Geometrie Convergence to e-z by Rational Functions with Real Poles.
Global smoothness preservation by some nonlinear max-product operators
Hermite interpolation: a survey of univariate computational methods.
Se considera la interpolación de Hermite de funciones de una variable mediante polinomios generalizados. Se pretende mostrar que técnicas computacionales conocidas para interpolación polinómica se pueden aplicar también a interpolación mediante polinomios generalizados. Como aplicación se estudia con cierto detalle la interpolación mediante funciones racionales con polos prefijados. La interpolación polinómica corresponde al caso particular en que todos los polos prefijados están en el infinito.
Higher order Schwarzian derivatives in interval dynamics
We introduce an infinite sequence of higher order Schwarzian derivatives closely related to the theory of monotone matrix functions. We generalize the classical Koebe lemma to maps with positive Schwarzian derivatives up to some order, obtaining control over derivatives of high order. For a large class of multimodal interval maps we show that all inverse branches of first return maps to sufficiently small neighbourhoods of critical values have their higher order Schwarzian derivatives positive up...
norm convergence of rational operators on the unit circle.
Linear prediction: Mathematics and engineering.
Maximally convergent rational approximants of meromorphic functions
Let f be meromorphic on the compact set E ⊂ C with maximal Green domain of meromorphy , ρ(f) < ∞. We investigate rational approximants of f on E with numerator degree ≤ n and denominator degree ≤ mₙ. We show that a geometric convergence rate of order on E implies uniform maximal convergence in m₁-measure inside if mₙ = o(n/log n) as n → ∞. If mₙ = o(n), n → ∞, then maximal convergence in capacity inside can be proved at least for a subsequence Λ ⊂ ℕ. Moreover, an analogue of Walsh’s...
Meromorphe Approximationen
Modulus of Approximate Continuity for R(X).
New characterization for nonlinear weighted best simultaneous approximation.
Nonlinear approximation in control problems
On Bernstein type rational functions of two variables