The main goal of this paper is to provide a brief survey of recent results, which connect together results from different areas of research. It is well known that numerical integration of functions with mixed smoothness is closely related to the discrepancy theory. We discuss this connection in detail and provide a general view of this connection. It was established recently that the new concept of fixed volume discrepancy is very useful in proving the upper bounds for the dispersion. Also, it was understood recently that point sets with small dispersion are very good for the universal discretization of the uniform norm of trigonometric polynomials.
Mots clés : numerical integration, discrepancy, dispersion, discretization, greedy algorithm
@article{SMAI-JCM_2019__S5__185_0, author = {Temlyakov, Vladimir}, title = {Connections between numerical integration, discrepancy, dispersion, and universal discretization}, journal = {The SMAI Journal of computational mathematics}, pages = {185--209}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {S5}, year = {2019}, doi = {10.5802/smai-jcm.58}, language = {en}, url = {http://www.numdam.org/articles/10.5802/smai-jcm.58/} }
TY - JOUR AU - Temlyakov, Vladimir TI - Connections between numerical integration, discrepancy, dispersion, and universal discretization JO - The SMAI Journal of computational mathematics PY - 2019 SP - 185 EP - 209 VL - S5 PB - Société de Mathématiques Appliquées et Industrielles UR - http://www.numdam.org/articles/10.5802/smai-jcm.58/ DO - 10.5802/smai-jcm.58 LA - en ID - SMAI-JCM_2019__S5__185_0 ER -
%0 Journal Article %A Temlyakov, Vladimir %T Connections between numerical integration, discrepancy, dispersion, and universal discretization %J The SMAI Journal of computational mathematics %D 2019 %P 185-209 %V S5 %I Société de Mathématiques Appliquées et Industrielles %U http://www.numdam.org/articles/10.5802/smai-jcm.58/ %R 10.5802/smai-jcm.58 %G en %F SMAI-JCM_2019__S5__185_0
Temlyakov, Vladimir. Connections between numerical integration, discrepancy, dispersion, and universal discretization. The SMAI Journal of computational mathematics, Tome S5 (2019), pp. 185-209. doi : 10.5802/smai-jcm.58. http://www.numdam.org/articles/10.5802/smai-jcm.58/
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