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  • 1
    Electronic Resource
    Electronic Resource
    On the failure of maximum entropy reconstruction for Fredholm equations and other infinite systems (1993)
    Springer
    Mathematical programming 61 (1993), S. 251-261 
    Details
    ISSN: 1436-4646
    Keywords: Primary 94A12, 90C48, 45B05 ; Secondary 94A27, 49J27 ; Boltzmann—Shannon entropy ; maximum entropy estimates ; Fenchel duality ; Fredholm equations ; Lagrange multipliers ; dual convex programs ; duality gaps ; regularization ; penalization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We analyse several examples where the maximum entropy solution to a system of equations exists but fails to satisfy the natural (dual) formula. These examples highlight the role that finiteness of the number of constraints has in the efficacy of maximum entropy type estimation and reconstruction. We also provide two regularization processes which repair the problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582150
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Convergence of decreasing sequences of convex sets in nonreflexive Banach spaces (1993)
    Springer
    Set-valued analysis 1 (1993), S. 355-363 
    Details
    ISSN: 1572-932X
    Keywords: Primary: 49A55, 90C25 ; secondary: 65K05, 49B27 ; Set convergence ; Mosco convergence ; slice convergence ; Wijsman convergence ; Painlevé-Kuratowski convergence ; moment problems ; inverse problems ; nonreflexive spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider nested sequences of linear or convex closed sets of the form arising in estimation and other inverse problems. We show that such sequences may fail to converge in any of the recently studied set convergences other than Mosco convergence. We also provide a positive result concerning the epislice convergence of related sequences of functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01027825
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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