Heidelberg 1999 – wissenschaftliches Programm
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A: Atomphysik
A 3: Spektroskopie II
A 3.5: Vortrag
Montag, 15. März 1999, 17:30–17:45, TE2
Numerische Techniken zur Konvergenzbeschleunigung und ihre Anwendung in der Theoretischen Atomphysik — •Jens Becher1, Ulrich Jentschura1, Peter Mohr2, Gerhard Soff1, and Ernst Weniger3 — 1Institut für Theroretische Physik, TU Dresden, 01062 Dresden — 2National Institute of Standards and Technology, Gaithersburg MD20899, USA — 3Institut für Physikalische und Theoretische Chemie, Universität Regensburg, 93040 Regensburg
We present numerical techniques to sum semiconvergent and/or divergent series to high accuracy. These series occur in theoretical physics and in scientific computing, and their summation to high accuracy without numerical loss is in most cases a yet unresolved problem. For these cases we present the Combined Nonlinear Condensation Transformation (CNCT), which is able to sum special series to high accuracy without loss of numerical significance. The enormous potential of the transformations will be demonstrated by numerical examples for the evaluation of certain slowly convergent series which arise in applied physics and problems which occur in the high-precision numerical calculation of quantum electrodynamic effects in hydrogenlike ions with low nuclear charge numbers.