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Digital inversive vectors can achieve polynomial tractability for the weighted star discrepancy and for multivariate integration

Abstract: We study high-dimensional numerical integration in the worstcase setting. The subject of tractability is concerned with the dependence of the worst-case integration error on the dimension. Roughly speaking, an integration problem is tractable if the worst-case error does not grow exponentially fast with the dimension. Many classical problems are known to be intractable. However, sometimes tractability can be shown. Often such proofs are based on randomly selected integration nodes. Of course, in applications, true random numbers are not available and hence one mimics them with pseudorandom number generators. This motivates us to propose the use of pseudorandom vectors as underlying integration nodes in order to achieve tractability. In particular, we consider digital inverse vectors and present two examples of problems, the weighted star discrepancy and integration of H¨older continuous, absolute convergent Fourier and cosine series, where the proposed method is successful.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

Fuente: Proc. Amer. Math. Soc. 145 (2017), 3297-3310

Editorial: American Mathematical Society

Año de publicación: 2017

Nº de páginas: 14

Tipo de publicación: Artículo de Revista

ISSN: 0002-9939,1088-6826

Autores/as

DICK, JOSEF

PILLICHSHAMMER, FRIEDRICH

WINTERHOF, ARNE