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Titel
High-dimensional algorithms-tractability and componentwise constructions / eingereicht von Helene Laimer
AutorInnenLaimer, Helene Anna
Beurteiler / BeurteilerinKritzer, Peter ; Dick, Josef
Betreuer / BetreuerinKritzer, Peter
ErschienenLinz, Juni 2017
Umfangix, 107 Seiten
HochschulschriftUniversität Linz, Dissertation, 2017
Anmerkung
Zusammenfassung in deutscher Sprache
In Zusammenarbeit mit dem Johann Radon Institute for Computational and Applied Mathematics
SpracheEnglisch
Bibl. ReferenzOeBB
DokumenttypDissertation
Schlagwörter (DE)multivariate Probleme / Tractability / komponentenweise Konstruktionen / Gitterpuntmengen / Quasi-Monte Carlo Methoden
Schlagwörter (EN)multivariate problems / tractability / componentwise constructions / lattice point sets / quasi-Monte Carlo methods
Schlagwörter (GND)Multivariate Analyse / Konstruktion / Differenzenverfahren / Monte-Carlo-Simulation
URNurn:nbn:at:at-ubl:1-17571 Persistent Identifier (URN)
Zugriffsbeschränkung
 Das Werk ist gemäß den "Hinweisen für BenützerInnen" verfügbar
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High-dimensional algorithms-tractability and componentwise constructions [0.79 mb]
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Zusammenfassung (Englisch)

In many applications, as for example physics, economics, finance and computational sciences, high-dimensional integration and approximation are problems which have to be solved numerically. In this thesis we study several aspects of high-dimensional solution algorithms for these problems.

In the first part of the thesis we consider tractability of multivariate continuous problems. This means that we are interested in how much information a numerical algorithm needs to solve the problem with accuracy . We study how fast the number of information evaluations required increases if the number of variables goes to infinity or the error demand tends to zero. We consider the two examples of a weighted Hermite space and of a hybrid function space.

In the second part of the thesis we investigate the problem of constructing point sets in the s-dimensional unit cube, which are used in a certain type of numerical algorithms, so-called quasi-Monte Carlo algorithms, which are widely used to numerically solve high-dimensional integration problems. We present several fast construction methods which provide point sets having certain good properties.

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