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Titolo:
Optimal experimental designs for linear inverse problems
Autore:
Liu, J;
Indirizzi:
UPS, UPMC, UMR 7608 CNRS, FAST Lab, F-91405 Orsay, France UPS Orsay France F-91405 UMR 7608 CNRS, FAST Lab, F-91405 Orsay, France
Titolo Testata:
INVERSE PROBLEMS IN ENGINEERING
fascicolo: 3, volume: 9, anno: 2001,
pagine: 287 - 314
SICI:
1068-2767(2001)9:3<287:OEDFLI>2.0.ZU;2-X
Fonte:
ISI
Lingua:
ENG
Soggetto:
SINGULAR-SYSTEM-ANALYSIS; REGULARIZATION; INFORMATION; EQUATIONS; CHOICE; NOISY;
Keywords:
optimal experimental design; inverse and ill-posed; nonlinear optimization; truncated singular value decomposition;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Engineering, Computing & Technology
Citazioni:
33
Recensione:
Indirizzi per estratti:
Indirizzo: Liu, J UPS, UPMC, UMR 7608 CNRS, FAST Lab, Batiment 502,Campus Univ, F-91405 Orsay, France UPS Batiment 502,Campus Univ Orsay France F-91405 05 Orsay, France
Citazione:
J. Liu, "Optimal experimental designs for linear inverse problems", INVERSE P E, 9(3), 2001, pp. 287-314

Abstract

Optimal experimental designs for inverse and ill-posed problems are investigated. Given discrete points s(i), for i = 1, ..., m, a Fredholm integral equation of the first kind can be discretized into a semi-discrete form g(s(i)) = integral (1)(0)k(s(i), t)f(t)dt by using a collocation method, and into a fully discrete form g(s(i)) = integral (1)(0)k(s(i) , t)f(n)(t)dt by restricting the unknown function f(n)(t) within an n-dimensional subspace. Our optimal design problem is to determine a distribution of the discrete points s(i), i = 1, ...,m maximizing the nth singular value lambda (n) of the semi-discrete or the fully discrete operators, where the number n plays the role of the regularization parameter (it could be fixed a priori or be selected a posteriori). The optimal experimental designs for various inverseproblems - numerical differentiation, inversion of Laplace transformation,small particles sizing by light extinction and two-dimensional steady-state inverse heat conduction problem, are studied numerically in detail. Several new and interesting features for the considered problems are found.

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Documento generato il 19/01/20 alle ore 09:01:39