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Titolo:
Optimal representation of multivariate functions or data in visualizable low-dimensional spaces
Autore:
Song, J;
Indirizzi:
Chinese Acad Engn, Beijing 100038, Peoples R China Chinese Acad Engn Beijing Peoples R China 100038 100038, Peoples R China
Titolo Testata:
CHINESE SCIENCE BULLETIN
fascicolo: 16, volume: 46, anno: 2001,
pagine: 1337 - 1345
SICI:
1001-6538(200108)46:16<1337:OROMFO>2.0.ZU;2-J
Fonte:
ISI
Lingua:
ENG
Keywords:
nonlinear integral equations; gradient operators; eigenvalues; orthonormal system of eigenfunctions; optimal approximation;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
22
Recensione:
Indirizzi per estratti:
Indirizzo: Song, J Chinese Acad Engn, Beijing 100038, Peoples R China Chinese Acad Engn Beijing Peoples R China 100038 Peoples R China
Citazione:
J. Song, "Optimal representation of multivariate functions or data in visualizable low-dimensional spaces", CHIN SCI B, 46(16), 2001, pp. 1337-1345

Abstract

It is intended to find the best representation of high-dimensional functions or multivariate data in L-2(Omega) with fewest number of terms, each of them is a combination of one-variable function. A system of nonlinear integral equations has been derived as an eigenvalue problem of gradient operator in the said space. It proved that the complete set of eigenfunctions generated by the gradient operator constitutes an orthonormal system, and any function of L-2(Omega) can be expanded with fewest terms and exponential rapidity of convergence. It is also proved as a corollary, the greatest eigenvalue of the integral operators has multiplicity 1 if the dimension of the underlying space R-n, n = 2, 4 and 6.

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Documento generato il 04/04/20 alle ore 08:05:33