Integration and approximation of multivariate functions: Average case complexity with isotropic wiener measure

G. W. Wasilkowski

doi:10.1090/S0273-0979-1993-00379-3

Integration and approximation of multivariate functions: Average case complexity with isotropic wiener measure

G. W. Wasilkowski

Computer Science

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20 Scopus citations

Abstract

We study the average case complexity of multivariate integration and L₂ function approximation for the class F = C([0, 1]^d) of continuous functions of d variables. The class F is endowed with the isotropic Wiener measure (Brownian motion in Levy’s sense). Furthermore, for both problems, only function values are used as data.

Original language	English
Pages (from-to)	308-314
Number of pages	7
Journal	Bulletin of the American Mathematical Society
Volume	28
Issue number	2
DOIs	https://doi.org/10.1090/S0273-0979-1993-00379-3
State	Published - Apr 1993

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0273-0979-1993-00379-3

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title = "Integration and approximation of multivariate functions: Average case complexity with isotropic wiener measure",

abstract = "We study the average case complexity of multivariate integration and L2 function approximation for the class F = C([0, 1]d) of continuous functions of d variables. The class F is endowed with the isotropic Wiener measure (Brownian motion in Levy{\textquoteright}s sense). Furthermore, for both problems, only function values are used as data.",

author = "Wasilkowski, \{G. W.\}",

year = "1993",

month = apr,

doi = "10.1090/S0273-0979-1993-00379-3",

language = "English",

volume = "28",

pages = "308--314",

number = "2",

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TY - JOUR

T1 - Integration and approximation of multivariate functions

T2 - Average case complexity with isotropic wiener measure

AU - Wasilkowski, G. W.

PY - 1993/4

Y1 - 1993/4

N2 - We study the average case complexity of multivariate integration and L2 function approximation for the class F = C([0, 1]d) of continuous functions of d variables. The class F is endowed with the isotropic Wiener measure (Brownian motion in Levy’s sense). Furthermore, for both problems, only function values are used as data.

AB - We study the average case complexity of multivariate integration and L2 function approximation for the class F = C([0, 1]d) of continuous functions of d variables. The class F is endowed with the isotropic Wiener measure (Brownian motion in Levy’s sense). Furthermore, for both problems, only function values are used as data.

UR - https://www.scopus.com/pages/publications/84967708645

UR - https://www.scopus.com/pages/publications/84967708645#tab=citedBy

U2 - 10.1090/S0273-0979-1993-00379-3

DO - 10.1090/S0273-0979-1993-00379-3

M3 - Comment/debate

AN - SCOPUS:84967708645

SN - 0273-0979

VL - 28

SP - 308

EP - 314

JO - Bulletin of the American Mathematical Society

JF - Bulletin of the American Mathematical Society

IS - 2

ER -

Integration and approximation of multivariate functions: Average case complexity with isotropic wiener measure

Abstract

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