Multivariate truncated moments problems and maximum entropy

被引：0
作者：
Calin -Grigore Ambrozie
机构：
[1] Institute of Mathematics of the Czech Academy,
[2] Institute of Mathematics “Simion Stoilow”-Romanian Academy,undefined
来源：
Analysis and Mathematical Physics | 2013年 / 3卷
关键词：
Moments problem; Representing measure; Entropy; Primary 44A60; Secondary 35A15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We characterize the existence of the Lebesgue integrable solutions of the truncated problem of moments in several variables on unbounded supports by the existence of some maximum entropy—type representing densities and discuss a few topics on their approximation in a particular case, of two variables and 4th order moments.
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页码：145 / 161
页数：16
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共 43 条
  • [1] Abramov RV(2010)The multidimensional maximum entropy moment problem: a review on numerical methods Commun. Math. Sci 8 377-392
  • [2] Ambrozie C.-G.(2003)Maximum entropy and moment problems Real Anal. Exch. 29 607-627
  • [3] Ambrozie C.-G.(2007)Finding positive matrices subject to linear restrictions Linear Algebra Appl. 426 2-3
  • [4] Bakonyi M(1995)Maximum entropy elements in the intersection of an affine space and the cone of positive definite matrices SIAM J. Matrix Anal. Appl. 16 369-376
  • [5] Woerdeman HJ(2008)Approximating integrals of multivariate exponentials: a moment approach Oper. Res. Lett. 36 205-210
  • [6] Bertsimas D(2012)Maximum entropy and feasibility methods for convex and nonconvex inverse problems, optimization J. Math. Program. Oper. Res. 61 1-338
  • [7] Doan XV(1991)Duality relationships for entropy-like minimization problems SIAM J. Cont. Optim. 29 325-3616
  • [8] Lasserre JB(2012)The truncated $$K$$ -moment problem for closure of open sets J. Funct. Anal. 263 3604-489
  • [9] Borwein J.M.(1981)Maximum entropy and conditional probability IEEE Trans. Inf. Theory. IT- 27 483-2731
  • [10] Borwein JM(2008)An analogue of the Riesz–Haviland theorem for the truncated moment problem J. Funct. Anal. 255 2709-65
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