Relative entropy and the multi-variable multi-dimensional moment problem
| dc.creator | Georgiou, Tryphon T. | |
| dc.date | 2005-06-07 | |
| dc.date.accessioned | 2026-07-07T09:51:08Z | |
| dc.date.available | 2026-07-07T09:51:08Z | |
| dc.description | Entropy-like functionals on operator algebras have been studied since the pioneering work of von Neumann, Umegaki, Lindblad, and Lieb. The most well-known are the von Neumann entropy $trace (ρ\log ρ)$ and a generalization of the Kullback-Leibler distance $trace (ρ\log ρ- ρ\log σ)$, refered to as quantum relative entropy and used to quantify distance between states of a quantum system. The purpose of this paper is to explore these as regularizing functionals in seeking solutions to multi-variable and multi-dimensional moment problems. It will be shown that extrema can be effectively constructed via a suitable homotopy. The homotopy approach leads naturally to a further generalization and a description of all the solutions to such moment problems. This is accomplished by a renormalization of a Riemannian metric induced by entropy functionals. As an application we discuss the inverse problem of describing power spectra which are consistent with second-order statistics, which has been the main motivation behind the present work. | |
| dc.description | 24 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0506124 | |
| dc.identifier | http://arxiv.org/abs/math/0506124 | |
| dc.identifier | IEEE Trans. on Information Theory, vol. 52(3): 1052 - 1066, March 2006. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165181 | |
| dc.subject | Optimization and Control | |
| dc.subject | 30E05 | |
| dc.title | Relative entropy and the multi-variable multi-dimensional moment problem | |
| dc.type | text |