Tractability of linear multivariate problems in the average case setting

Fred Hickernell; Greg Wasilkowski; Henryk Wózniakowski

doi:10.1007/978-3-540-74496-2_27

Tractability of linear multivariate problems in the average case setting

Fred Hickernell, Greg Wasilkowski, Henryk Wózniakowski

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

24 Scopus citations

Abstract

We study the average case setting for linear multivariate problems defined over a separable Banach space of functions f of d variables. The Banach space is equipped with a Gaussian measure. We approximate linear multivariate problems by computing finitely many information evaluations. An information evaluation is defined as an evaluation of a continuous linear functional from a given class A. We consider two classes of information evaluations; the first class A ^all consists of all continuous linear functionals, and the second class A^std consists of function evaluations.

Original language	English
Title of host publication	Monte Carlo and Quasi-Monte Carlo Methods 2006
Pages	461-493
Number of pages	33
DOIs	https://doi.org/10.1007/978-3-540-74496-2_27
State	Published - 2008
Event	7th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2006 - Ulm, Germany Duration: Aug 14 2006 → Aug 18 2006

Publication series

Name	Monte Carlo and Quasi-Monte Carlo Methods 2006

Conference

Conference	7th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2006
Country/Territory	Germany
City	Ulm
Period	8/14/06 → 8/18/06

ASJC Scopus subject areas

Applied Mathematics

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10.1007/978-3-540-74496-2_27

Cite this

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title = "Tractability of linear multivariate problems in the average case setting",

abstract = "We study the average case setting for linear multivariate problems defined over a separable Banach space of functions f of d variables. The Banach space is equipped with a Gaussian measure. We approximate linear multivariate problems by computing finitely many information evaluations. An information evaluation is defined as an evaluation of a continuous linear functional from a given class A. We consider two classes of information evaluations; the first class A all consists of all continuous linear functionals, and the second class Astd consists of function evaluations.",

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Hickernell, F, Wasilkowski, G & Wózniakowski, H 2008, Tractability of linear multivariate problems in the average case setting. in Monte Carlo and Quasi-Monte Carlo Methods 2006. Monte Carlo and Quasi-Monte Carlo Methods 2006, pp. 461-493, 7th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2006, Ulm, Germany, 8/14/06. https://doi.org/10.1007/978-3-540-74496-2_27

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AU - Wasilkowski, Greg

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AB - We study the average case setting for linear multivariate problems defined over a separable Banach space of functions f of d variables. The Banach space is equipped with a Gaussian measure. We approximate linear multivariate problems by computing finitely many information evaluations. An information evaluation is defined as an evaluation of a continuous linear functional from a given class A. We consider two classes of information evaluations; the first class A all consists of all continuous linear functionals, and the second class Astd consists of function evaluations.

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T3 - Monte Carlo and Quasi-Monte Carlo Methods 2006

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BT - Monte Carlo and Quasi-Monte Carlo Methods 2006

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Tractability of linear multivariate problems in the average case setting

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