Austrian Academy of Sciences
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LH III C Chronology and Synchronisms III. LH IIIC Late and the Transition to the Early Iron Age. Proceedings of the international workshop held at the Austrian Academy of Sciences at Vienna February 23rd and 24th, 2007
Transformed rank-1 lattices for high-dimensional approximation. ETNA - Electronic Transactions on Numerical Analysis
This paper describes an extension of Fourier approximation methods for multivariate functions defined on thetorus to functions in a weighted Hilbert space via a multivariate change of variables .We establish sufficient conditions for and such that the composition of a function in such a weighted Hilbert space with yields a function in theSobolev space of functions on the torus with mixed smoothness of natural order .In this approach we adapt algorithms for the evaluation and reconstruction of multivariate trigonometric polynomials on the torus based on single and multiple reconstructing rank- lattices.Since in applications it may be difficult to choose a related function space, we make use of dimension incremental construction methods for sparse frequency sets.Various numerical tests confirm the obtained theoretical results for the transformed methods
Incomplete beta polynomials. ETNA - Electronic Transactions on Numerical Analysis
We study some properties of incomplete beta polynomials, in particular, their zero asymptotic distribution. These polynomials satisfy a three-term recurrence relation, so they can be written as the sum of two terms each one leading to their asymptotic behavior in a region