Maximum entropy in the problem of moments

Journal Article · Wed Aug 01 04:00:00 EDT 1984 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526446· OSTI ID:6948797

Mead, L R; Papanicolaou, N

The maximum-entropy approach to the solution of underdetermined inverse problems is studied in detail in the context of the classical moment problem. In important special cases, such as the Hausdorff moment problem, we establish necessary and sufficient conditions for the existence of a maximum-entropy solution and examine the convergence of the resulting sequence of approximations. A number of explicit illustrations are presented. In addition to some elementary examples, we analyze the maximum-entropy reconstruction of the density of states in harmonic solids and of dynamic correlation functions in quantum spin systems. We also briefly indicate possible applications to the Lee--Yang theory of Ising models, to the summation of divergent series, and so on. The general conclusion is that maximum entropy provides a valuable approximation scheme, a serious competitor of traditional Pade-like procedures.

• Research Organization: Department of Physics, Washington University, St. Louis, Missouri 63130
• OSTI ID: 6948797
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 25:8; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

656000 -- Condensed Matter Physics
658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CORRELATION FUNCTIONS
CRYSTAL MODELS
ELECTRONIC EQUIPMENT
ENERGY LEVELS
ENTROPY
EQUIPMENT
FUNCTIONS
HARMONIC OSCILLATORS
HAUSDORFF SPACE
HEISENBERG MODEL
ISING MODEL
LEE-YANG THEORY
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MATHEMATICS
NUMERICAL ANALYSIS
OSCILLATORS
PHYSICAL PROPERTIES
SPACE
THERMODYNAMIC PROPERTIES
USES