Maximum entropy in the problem of moments

Lawrence R. Mead; N. Papanicolaou

doi:10.1063/1.526446

journal article Aug 01, 1984

Maximum entropy in the problem of moments

Lawrence R. Mead N. Papanicolaou

Journal of Mathematical Physics Vol. 25 No. 8 pp. 2404-2417 · AIP Publishing

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Abstract

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 Padé-like procedures.

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Details

Published: Aug 01, 1984
Vol/Issue: 25(8)
Pages: 2404-2417

Authors

L

Lawrence R. Mead

Department of Physics, Washington University, St. Louis, Missouri 63130

N

N. Papanicolaou

Department of Physics, Washington University, St. Louis, Missouri 63130

Cite This Article

Lawrence R. Mead, N. Papanicolaou (1984). Maximum entropy in the problem of moments. Journal of Mathematical Physics, 25(8), 2404-2417. https://doi.org/10.1063/1.526446

Maximum entropy in the problem of moments

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