Complexity of oscillatory integrals on the real line

Erich Novak; Mario Ullrich; Henryk Wozniakowski; Shun Zhang

doi:10.1007/s10444-016-9496-6

Complexity of oscillatory integrals on the real line

Erich Novak
, Mario Ullrich
, Henryk Wozniakowski
, Shun Zhang

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

Abstract

We analyze univariate oscillatory integrals defined on the real line for functions from the standard Sobolev space H^s(R) and from the space C^s(R) with an arbitrary integer s ≥ 1. We find tight upper and lower bounds for the worst case error of optimal algorithms that use n function values.

Original language	English
Pages (from-to)	537-553
Number of pages	16
Journal	Advances in Computational Mathematics
Volume	43
Issue number	3
DOIs	https://doi.org/10.1007/s10444-016-9496-6
Publication status	Published - 2017

Fields of science

101002 Analysis
101032 Functional analysis

JKU Focus areas

Computation in Informatics and Mathematics

Access to Document

10.1007/s10444-016-9496-6

Cite this

@article{fce2381c37ae40a7a6f2dcd5cc698b9c,

title = "Complexity of oscillatory integrals on the real line",

abstract = "We analyze univariate oscillatory integrals defined on the real line for functions from the standard Sobolev space H\textasciicircum{}s(R) and from the space C\textasciicircum{}s(R) with an arbitrary integer s ≥ 1. We find tight upper and lower bounds for the worst case error of optimal algorithms that use n function values.",

author = "Erich Novak and Mario Ullrich and Henryk Wozniakowski and Shun Zhang",

year = "2017",

doi = "10.1007/s10444-016-9496-6",

language = "English",

volume = "43",

pages = "537--553",

journal = "Advances in Computational Mathematics",

issn = "1572-9044",

publisher = "Spinger US",

number = "3",

}

TY - JOUR

T1 - Complexity of oscillatory integrals on the real line

AU - Novak, Erich

AU - Ullrich, Mario

AU - Wozniakowski, Henryk

AU - Zhang, Shun

PY - 2017

Y1 - 2017

N2 - We analyze univariate oscillatory integrals defined on the real line for functions from the standard Sobolev space H^s(R) and from the space C^s(R) with an arbitrary integer s ≥ 1. We find tight upper and lower bounds for the worst case error of optimal algorithms that use n function values.

AB - We analyze univariate oscillatory integrals defined on the real line for functions from the standard Sobolev space H^s(R) and from the space C^s(R) with an arbitrary integer s ≥ 1. We find tight upper and lower bounds for the worst case error of optimal algorithms that use n function values.

UR - https://www.scopus.com/pages/publications/84994727993

U2 - 10.1007/s10444-016-9496-6

DO - 10.1007/s10444-016-9496-6

M3 - Article

SN - 1572-9044

VL - 43

SP - 537

EP - 553

JO - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

IS - 3

ER -

Complexity of oscillatory integrals on the real line

Abstract

Fields of science

JKU Focus areas

Access to Document

Other files and links

Cite this