Austrian Academy of Sciences

Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschaften
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    9783700139508-Textband Gesamt.pdf

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    Transformed rank-1 lattices for high-dimensional approximation. ETNA - Electronic Transactions on Numerical Analysis

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    This paper describes an extension of Fourier approximation methods for multivariate functions defined on thetorus mathbbTd\\mathbb{T}^d to functions in a weighted Hilbert space L2(mathbbRd,omega)L_{2}(\\mathbb{R}^d, \\omega)via a multivariate change of variables psi:left(frac12,frac12right)dtomathbbRd\\psi:\\left(-\\frac{1}{2},\\frac{1}{2}\\right)^d\\to\\mathbb{R}^d.We establish sufficient conditions for psi\\psi and omega\\omega such that the composition of a function in such a weighted Hilbert space with psi\\psi yields a function in theSobolev space Hrmmixm(mathbbTd)H_{\\rm mix}^{m}(\\mathbb{T}^d) of functions on the torus with mixed smoothness of natural order minmathbbN0m \\in \\mathbb{N}_{0}.In this approach we adapt algorithms for the evaluation and reconstruction of multivariate trigonometric polynomials on the torus mathbbTd\\mathbb{T}^dbased on single and multiple reconstructing rank-11 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

    Laudatio für Spyros Iakovidis

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    Incomplete beta polynomials. ETNA - Electronic Transactions on Numerical Analysis

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    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

    ANNEXES: LIST OF INTERVIEWEES - VIENNA - ATHENS

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    ONIX21-Feed. Other Online Editions|Was kommt nach dem Higgs-Boson?|

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