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

Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

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.

Originalsprache	Englisch
Seiten (von - bis)	537-553
Seitenumfang	17
Fachzeitschrift	Advances in Computational Mathematics
Volume	43
Ausgabenummer	3
DOIs	https://doi.org/10.1007/s10444-016-9496-6
Publikationsstatus	Veröffentlicht - 01 Juni 2017

Wissenschaftszweige

101002 Analysis
101032 Funktionalanalysis

JKU-Schwerpunkte

Computation in Informatics and Mathematics

Zugriff auf Dokument

10.1007/s10444-016-9496-6

Andere Dateien und Links

Verknüpfung zur Publikation in Scopus

Dieses zitieren

@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",

month = jun,

day = "1",

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 - 2017/6/1

Y1 - 2017/6/1

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 -