Mean Squared Error Minimization for Inverse Moment Problems
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Mean Squared Error Minimization for Inverse Moment Problems
Original language description
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
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BB - Applied statistics, operational research
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA13-06894S" target="_blank" >GA13-06894S: Semidefinite programming for polynomial optimal control problems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applied Mathematics & Optimization
ISSN
0095-4616
e-ISSN
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Volume of the periodical
70
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
28
Pages from-to
83-110
UT code for WoS article
000339107200004
EID of the result in the Scopus database
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