On applicability of the sparse grid method in the worst case setting

Fengbo Hang; Youming Li

doi:10.1007/s11075-006-9025-7

On applicability of the sparse grid method in the worst case setting

Fengbo Hang, Youming Li

Mathematics

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

Abstract

Let T_k: W^rk_p → W^sk _q be bounded linear operators. We provide several sufficient conditions for the validity of the inequality ∥ ⊗k T_k ∥ ≤ Π_k ∥ T_k. These results can be applied to error and cost estimates for the sparse grid method.

Original language	English (US)
Pages (from-to)	95-105
Number of pages	11
Journal	Numerical Algorithms
Volume	42
Issue number	2
DOIs	https://doi.org/10.1007/s11075-006-9025-7
State	Published - Jun 2006

Keywords

Information-based complexity
Smolyak's algorithm
Sparse grid method

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s11075-006-9025-7

Cite this

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title = "On applicability of the sparse grid method in the worst case setting",

abstract = "Let Tk: Wrkp → Wsk q be bounded linear operators. We provide several sufficient conditions for the validity of the inequality ∥ ⊗k Tk ∥ ≤ Πk ∥ Tk. These results can be applied to error and cost estimates for the sparse grid method.",

keywords = "Information-based complexity, Smolyak's algorithm, Sparse grid method",

author = "Fengbo Hang and Youming Li",

year = "2006",

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AU - Li, Youming

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AB - Let Tk: Wrkp → Wsk q be bounded linear operators. We provide several sufficient conditions for the validity of the inequality ∥ ⊗k Tk ∥ ≤ Πk ∥ Tk. These results can be applied to error and cost estimates for the sparse grid method.

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KW - Smolyak's algorithm

KW - Sparse grid method

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On applicability of the sparse grid method in the worst case setting

Abstract

Keywords

ASJC Scopus subject areas

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