3,626 research outputs found
Finitely additive extensions of distribution functions and moment sequences: The coherent lower prevision approach
We study the information that a distribution function provides about the finitely additive probability measure inducing it. We show that in general there is an infinite number of finitely additive probabilities associated with the same distribution function. Secondly, we investigate the relationship between a distribution function and its given sequence of moments. We provide formulae for the sets of distribution functions, and finitely additive probabilities, associated with some moment sequence, and determine under which conditions the moments determine the distribution function uniquely. We show that all these problems can be addressed efficiently using the theory of coherent lower previsions
Convergence Acceleration via Combined Nonlinear-Condensation Transformations
A method of numerically evaluating slowly convergent monotone series is
described. First, we apply a condensation transformation due to Van Wijngaarden
to the original series. This transforms the original monotone series into an
alternating series. In the second step, the convergence of the transformed
series is accelerated with the help of suitable nonlinear sequence
transformations that are known to be particularly powerful for alternating
series. Some theoretical aspects of our approach are discussed. The efficiency,
numerical stability, and wide applicability of the combined
nonlinear-condensation transformation is illustrated by a number of examples.
We discuss the evaluation of special functions close to or on the boundary of
the circle of convergence, even in the vicinity of singularities. We also
consider a series of products of spherical Bessel functions, which serves as a
model for partial wave expansions occurring in quantum electrodynamic bound
state calculations.Comment: 24 pages, LaTeX, 12 tables (accepted for publication in Comput. Phys.
Comm.
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