Mean Squared Error Minimization for Inverse Moment Problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F14%3A00218836" target="_blank" >RIV/68407700:21230/14:00218836 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00245-013-9235-z" target="_blank" >http://dx.doi.org/10.1007/s00245-013-9235-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00245-013-9235-z" target="_blank" >10.1007/s00245-013-9235-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Mean Squared Error Minimization for Inverse Moment Problems

Popis výsledku v původním jazyce

We consider the problem of approximating the unknown density of a measure on , absolutely continuous with respect to some given reference measure , only from the knowledge of finitely many moments of . Given and moments of order , we provide a polynomialwhich minimizes the mean square error over all polynomials of degree at most . If there is no additional requirement, is obtained as solution of a linear system. In addition, if is expressed in the basis of polynomials that are orthonormal with respectto , its vector of coefficients is just the vector of given moments and no computation is needed. Moreover in as . In general nonnegativity of is not guaranteed even though is nonnegative. However, with this additional nonnegativity requirement one obtains analogous results but computing that minimizes now requires solving an appropriate semidefinite program. We have tested the approach on some applications arising from the reconstruction of geometrical objects and the approximation of s

Název v anglickém jazyce

Mean Squared Error Minimization for Inverse Moment Problems

Popis výsledku anglicky

We consider the problem of approximating the unknown density of a measure on , absolutely continuous with respect to some given reference measure , only from the knowledge of finitely many moments of . Given and moments of order , we provide a polynomialwhich minimizes the mean square error over all polynomials of degree at most . If there is no additional requirement, is obtained as solution of a linear system. In addition, if is expressed in the basis of polynomials that are orthonormal with respectto , its vector of coefficients is just the vector of given moments and no computation is needed. Moreover in as . In general nonnegativity of is not guaranteed even though is nonnegative. However, with this additional nonnegativity requirement one obtains analogous results but computing that minimizes now requires solving an appropriate semidefinite program. We have tested the approach on some applications arising from the reconstruction of geometrical objects and the approximation of s

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BB - Aplikovaná statistika, operační výzkum

OECD FORD obor

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Projekt

<a href="/cs/project/GA13-06894S" target="_blank" >GA13-06894S: Semidefinitní programování pro polynomiální problémy optimálního řízení</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Applied Mathematics & Optimization

ISSN

0095-4616

e-ISSN

—

Svazek periodika

70

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

28

Strana od-do

83-110

Kód UT WoS článku

000339107200004

EID výsledku v databázi Scopus

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