Optimal quadrature for haar wavelet spaces

Stefan Heinrich; Fred J. Hickernell; Rong Xian Yue

doi:10.1090/S0025-5718-03-01531-X

Optimal quadrature for haar wavelet spaces

Stefan Heinrich^*, Fred J. Hickernell, Rong Xian Yue

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

This article considers the error of the scrambled equidistribution quadrature rules in the worst-case, random-case, and average-case settings. The underlying space of integrands is a Hilbert space of multidimensional Haar wavelet series, ℋ_wav. The asymptotic orders of the errors are derived for the case of the scrambled (λ, t, m, s)-nets and (t, s)-sequences. These rules are shown to have the best asymptotic convergence rates for any random quadrature rule for the space of integrands ℋ _wav.

Original language	English
Pages (from-to)	259-277
Number of pages	19
Journal	Mathematics of Computation
Volume	73
Issue number	245
DOIs	https://doi.org/10.1090/S0025-5718-03-01531-X
Publication status	Published - Jan 2004
Externally published	Yes

Scopus Subject Areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

User-Defined Keywords

High dimensional integration
Lower bounds
Monte Carlo methods
Quasi-Monte Carlo methods

Access to Document

10.1090/S0025-5718-03-01531-X

Cite this

@article{f294b3ed231f48b4a15f9b3f59b6fbca,

title = "Optimal quadrature for haar wavelet spaces",

abstract = "This article considers the error of the scrambled equidistribution quadrature rules in the worst-case, random-case, and average-case settings. The underlying space of integrands is a Hilbert space of multidimensional Haar wavelet series, ℋwav. The asymptotic orders of the errors are derived for the case of the scrambled (λ, t, m, s)-nets and (t, s)-sequences. These rules are shown to have the best asymptotic convergence rates for any random quadrature rule for the space of integrands ℋ wav.",

keywords = "High dimensional integration, Lower bounds, Monte Carlo methods, Quasi-Monte Carlo methods",

author = "Stefan Heinrich and Hickernell, {Fred J.} and Yue, {Rong Xian}",

year = "2004",

month = jan,

doi = "10.1090/S0025-5718-03-01531-X",

language = "English",

volume = "73",

pages = "259--277",

journal = "Mathematics of Computation",

issn = "0025-5718",

publisher = "American Mathematical Society",

number = "245",

}

TY - JOUR

T1 - Optimal quadrature for haar wavelet spaces

AU - Heinrich, Stefan

AU - Hickernell, Fred J.

AU - Yue, Rong Xian

PY - 2004/1

Y1 - 2004/1

N2 - This article considers the error of the scrambled equidistribution quadrature rules in the worst-case, random-case, and average-case settings. The underlying space of integrands is a Hilbert space of multidimensional Haar wavelet series, ℋwav. The asymptotic orders of the errors are derived for the case of the scrambled (λ, t, m, s)-nets and (t, s)-sequences. These rules are shown to have the best asymptotic convergence rates for any random quadrature rule for the space of integrands ℋ wav.

AB - This article considers the error of the scrambled equidistribution quadrature rules in the worst-case, random-case, and average-case settings. The underlying space of integrands is a Hilbert space of multidimensional Haar wavelet series, ℋwav. The asymptotic orders of the errors are derived for the case of the scrambled (λ, t, m, s)-nets and (t, s)-sequences. These rules are shown to have the best asymptotic convergence rates for any random quadrature rule for the space of integrands ℋ wav.

KW - High dimensional integration

KW - Lower bounds

KW - Monte Carlo methods

KW - Quasi-Monte Carlo methods

UR - https://www.jstor.org/stable/4099869

UR - http://www.scopus.com/inward/record.url?scp=0942278836&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-03-01531-X

DO - 10.1090/S0025-5718-03-01531-X

M3 - Article

AN - SCOPUS:0942278836

SN - 0025-5718

VL - 73

SP - 259

EP - 277

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 245

ER -

Optimal quadrature for haar wavelet spaces

Abstract

Scopus Subject Areas

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this