Minimizing the L2 and L∞ star discrepancies of a single point in the unit hypercube

Consider a point set that contains a single point x in the s-dimensional hypercube. We show where to place x in order to minimize the L2 and L~ star discrepancies, measures often used in quasi-Monte Carlo integration.

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Bibliographische Detailangaben
Veröffentlicht in:	Journal of computational and applied mathematics 2006-12, Vol.197 (1), p.282-285
Hauptverfasser:	PILLARDS, Tim, VANDEWOESTYNE, Bart, COOLS, Ronald
Format:	Artikel
Sprache:	eng
Schlagworte:	Calculus of variations and optimal control Exact sciences and technology Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation Numerical methods in probability and statistics Sciences and techniques of general use
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Beschreibung
Zusammenfassung:	Consider a point set that contains a single point x in the s-dimensional hypercube. We show where to place x in order to minimize the L2 and L~ star discrepancies, measures often used in quasi-Monte Carlo integration.
ISSN:	0377-0427 1879-1778
DOI:	10.1016/j.cam.2005.11.005