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On properties of the iterative maximum likelihood reconstruction method
Author(s) -
Mülthei H. N.,
Schorr B.,
Törnig W.
Publication year - 1989
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670110303
Subject(s) - mathematics , iterative method , divergence (linguistics) , convergence (economics) , kernel (algebra) , kernel density estimation , mathematical optimization , algorithm , pure mathematics , statistics , philosophy , linguistics , estimator , economics , economic growth
In this paper, we continue our investigations 6 on the iterative maximum likelihood reconstruction method applied to a special class of integral equations of the first kind, where one of the essential assumptions is the positivity of the kernel and the given right‐hand side. Equations of this type often occur in connection with the determination of density functions from measured data. There are certain relations between the directed Kullback–Leibler divergence and the iterative maximum likelihood reconstruction method some of which were already observed by other authors. Using these relations, further properties of the iterative scheme are shown and, in particular, a new short and elementary proof of convergence of the iterative method is given for the discrete case. Numerical examples have already been given in References 6. Here, an example is considered which can be worked out analytically and which demonstrates fundamental properties of the algorithm.