Geodesic
Numerical Analysis
Resolution of the finite Markov moment problem
[Résolution du problème fini des moments de Markov]

Présenté par : Philippe G. Ciarlet

Gosse, Laurent1 ; Runborg, Olof2
1 IAC-CNR “Mauro Picone” (sezione di Bari), Via Amendola 122/D, 70126 Bari, Italy
2 NADA, KTH, 10044 Stockholm, Sweden
Comptes Rendus. Mathématique, Tome 341 (2005) no. 12, pp. 775-780.

Voir la notice de l'article provenant de la source Numdam

We expose in full detail a constructive procedure to invert the so-called ‘finite Markov moment problem’. The proofs rely on the general theory of Toeplitz matrices together with the classical Newton's relations.

Nous présentons en détail une procédure constructive pour inverser le « problème fini des moments de Markov ». Les preuves reposent sur la théorie générale des matrices de Toeplitz et les classiques relations de Newton.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.10.009

Gosse, Laurent 1 ; Runborg, Olof 2

1 IAC-CNR “Mauro Picone” (sezione di Bari), Via Amendola 122/D, 70126 Bari, Italy
2 NADA, KTH, 10044 Stockholm, Sweden 
@article{CRMATH_2005__341_12_775_0,
     author = {Gosse, Laurent and Runborg, Olof},
     title = {Resolution of the finite {Markov} moment problem},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {775--780},
     publisher = {Elsevier},
     volume = {341},
     number = {12},
     year = {2005},
     doi = {10.1016/j.crma.2005.10.009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2005.10.009/}
}
TY  - JOUR
AU  - Gosse, Laurent
AU  - Runborg, Olof
TI  - Resolution of the finite Markov moment problem
JO  - Comptes Rendus. Mathématique
PY  - 2005
SP  - 775
EP  - 780
VL  - 341
IS  - 12
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2005.10.009/
DO  - 10.1016/j.crma.2005.10.009
LA  - en
ID  - CRMATH_2005__341_12_775_0
ER  - 
%0 Journal Article
%A Gosse, Laurent
%A Runborg, Olof
%T Resolution of the finite Markov moment problem
%J Comptes Rendus. Mathématique
%D 2005
%P 775-780
%V 341
%N 12
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2005.10.009/
%R 10.1016/j.crma.2005.10.009
%G en
%F CRMATH_2005__341_12_775_0
Gosse, Laurent; Runborg, Olof. Resolution of the finite Markov moment problem. Comptes Rendus. Mathématique, Tome 341 (2005) no. 12, pp. 775-780. doi : 10.1016/j.crma.2005.10.009. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2005.10.009/

[1] D. Bini, Polynomial and Matrix Computations. I. Fundamental Algorithms, Birkhaüser

[2] Brenier, Y. Équations de moment et conditions d'entropie pour des modèles cinétiques, Séminaire sur les Équations aux Dérivées Partielles, 1994–1995, Exp. No. XXII, École Polytech., Palaiseau, 1995 (11 p)

[3] Brenier, Y.; Corrias, L. A kinetic formulation for multibranch entropy solutions of scalar conservation laws, Ann. Inst. H. Poincaré Anal. Non Linéare, Volume 15 (1998), pp. 169-190

[4] P. Diaconis, D. Friedman, The Markov moment problem and de Finetti's theorem, Math. Z., in press

[5] Gosse, L. Using K-branch entropy solutions for multivalued geometric optics computations, J. Comp. Phys., Volume 180 (2002), pp. 155-182

[6] Gosse, L.; Runborg, O. Finite moment problems and applications to multiphase computations in geometric optics, Comm. Math. Sci., Volume 3 (2005), pp. 373-392

[7] Hepstein, I.N. Topics in Algebra, Ginn Waltham, Massachusetts, 1964 (p. 208)

[8] Korobov, V.I.; Sklyar, G.M. Time-optimality and the power moment problem, Mat. Sb. (N.S.), Volume 134 (1987) no. 176, pp. 186-206 287 (in Russian) Translation in Math. USSR-Sb., 62, 1, 1989, pp. 185-206

[9] Krein, M.G.; Nudel'man, A.A. The Markov Moment Problem and Extremal Problems, Amer. Math. Soc. Transl., Amer. Math. Soc., Providence, RI, 1977

[10] Lewis, A.S. Superresolution in the Markov moment problem, J. Math. Anal. Appl., Volume 197 (1996), pp. 774-780

[11] Runborg, O. Some new results in multiphase geometrical optics, Math. Mod. Numer. Anal., Volume 34 (2000), pp. 1203-1231

[12] Sklyar, G.M.; Fardigola, L.V. The Markov power moment problem in problems of controllability and frequency extinguishing for the wave equation on a half-axis, J. Math. Anal. Appl., Volume 276 (2002), pp. 109-134

[13] Talenti, G. Recovering a function from a finite number of moments, Inverse Problems, Volume 3 (1987), pp. 501-517

Cité par Sources :