Optimization of Burg's entropy over linear constraints

Yair Censor; Alvaro R. De Pierro; Alfredo N. Iusem

doi:10.1016/0168-9274(91)90059-9

Optimization of Burg's entropy over linear constraints

Yair Censor, Alvaro R. De Pierro, Alfredo N. Iusem

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Two special-purpose iterative algorithms for maximization of Burg's entropy function subject to linear inequalities are presented. Both are "row-action" methods which use in each iteration the information contained in only one constraint. One is an underrelaxed Bregman algorithm which requires, at each iterative step, the solution of a system of equations. In contrast with this, the second algorithm employs a closed-form formula for the iterative step. Complete analyses of the convergence for both algorithms are given.

Original language	English
Pages (from-to)	151-165
Number of pages	15
Journal	Applied Numerical Mathematics
Volume	7
Issue number	2
DOIs	https://doi.org/10.1016/0168-9274(91)90059-9
State	Published - Feb 1991

Bibliographical note

Funding Information:
Part of this work was done during a visit of Y. Censor to the Instituto de Matematica Pura e Aplicada (IMPA) in Rio de Janeiro, Brazil. We thank Professor Lindolpho de Carvalho Dias, Director of IMPA, for making this visit possible. The research of Y. Censor has been also supported by NIH grant HL-28438 while visiting the Medical Image Processing Group (MIPG) at the Department of Radiology. Hospital of the University of Pennsylvania, Philadelphia, PA.

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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N2 - Two special-purpose iterative algorithms for maximization of Burg's entropy function subject to linear inequalities are presented. Both are "row-action" methods which use in each iteration the information contained in only one constraint. One is an underrelaxed Bregman algorithm which requires, at each iterative step, the solution of a system of equations. In contrast with this, the second algorithm employs a closed-form formula for the iterative step. Complete analyses of the convergence for both algorithms are given.

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Optimization of Burg's entropy over linear constraints

Abstract

Bibliographical note

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