Méthodes de réalisation de produit scalaire et de problème de moments avec maximisation d'entropie

Valerie Girardin

Studia Mathematica (1997)

  • Volume: 124, Issue: 3, page 199-213
  • ISSN: 0039-3223

Abstract

top
We develop several methods of realization of scalar product and generalized moment problems. Constructions are made by use of a Hilbertian method or a fixed point method. The constructed solutions are rational fractions and exponentials of polynomials. They are connected to entropy maximization. We give the general form of the maximizing solution. We show how it is deduced from the maximizing solution of the algebraic moment problem.

How to cite

top

Girardin, Valerie. "Méthodes de réalisation de produit scalaire et de problème de moments avec maximisation d'entropie." Studia Mathematica 124.3 (1997): 199-213. <http://eudml.org/doc/216409>.

@article{Girardin1997,
author = {Girardin, Valerie},
journal = {Studia Mathematica},
keywords = {moments; scalar product; entropy maximization; realization of scalar product and generalized moment problems; Hilbertian method; fixed point method; rational fractions; exponentials of polynomials; maximizing solution; algebraic moment problem},
language = {fre},
number = {3},
pages = {199-213},
title = {Méthodes de réalisation de produit scalaire et de problème de moments avec maximisation d'entropie},
url = {http://eudml.org/doc/216409},
volume = {124},
year = {1997},
}

TY - JOUR
AU - Girardin, Valerie
TI - Méthodes de réalisation de produit scalaire et de problème de moments avec maximisation d'entropie
JO - Studia Mathematica
PY - 1997
VL - 124
IS - 3
SP - 199
EP - 213
LA - fre
KW - moments; scalar product; entropy maximization; realization of scalar product and generalized moment problems; Hilbertian method; fixed point method; rational fractions; exponentials of polynomials; maximizing solution; algebraic moment problem
UR - http://eudml.org/doc/216409
ER -

References

top
  1. [1] R. Azencott et D. Dacunha-Castelle, Séries d'observations irrégulières, Masson, 1984 Zbl0546.62060
  2. [2] A. Ben-Tal and A. Charnes, A dual optimization framework for some problems of information theory and statistics, Problems Control Inform. Theory 8 (1979), 387-401. Zbl0437.90078
  3. [3] J. M. Borwein and A. S. Lewis, Duality relationships for entropy-like minimization problems, SIAM J. Control Optim. 29 (1991), 325-338. Zbl0797.49030
  4. [4] I. Csiszár, I-divergence geometry of probability distributions and minimization problems, Ann. Probab. 3 (1975), 146-158. Zbl0318.60013
  5. [5] A. Devinatz, Integral representations of positive definite functions, II, Trans. Amer. Math. Soc. 77 (1954), 455-480. Zbl0058.33201
  6. [6] V. Girardin, Problème des moments et entropie. Application en probabilités, thèse, Univ. Paris-Sud, 1991. 
  7. [7] S. Ihara, Maximum entropy spectral analysis and ARMA processes, IEEE Trans. Inform. Theory 30 (1984), 377-380. Zbl0539.62100
  8. [8] M. Kreĭn and A. Nudel'man, The Markov Moment Problem and Extremal Problems, Amer. Math. Soc., 1977. 
  9. [9] H. Landau, Maximum entropy and the moment problem, Bull. Amer. Math. Soc. 16 (1987), 47-77. Zbl0617.42004
  10. [10] A. Lippman, A maximum entropy method for expert system construction, in: Maximum-Entropy and Bayesian Methods in Science and Engineering, Vol. 2, Kluwer, 1988, 243-263. 
  11. [11] A. Seghier, Extension de fonctions de type positif et entropie associée. Cas multidimensionnel, Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991), 651-675. Zbl0776.42015
  12. [12] A. Seghier, Extension de fonctions de type positif. Cas continu, Prépub. Univ. Paris-Sud, 1989. Zbl0691.42014

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.