State space formulas for a suboptimal rational Leech problem I: Maximum entropy solution

2014/08/09 by A. E. Frazho, Frazho, A. E., S. ter Horst +3
Mathematics · #47A56 #93B15 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47A57 #Secondary 47A68 #math.FA #msc:47A56 #msc:47A57 #msc:47A68 #msc:93B15

paper · pdf · doi:10.48550/arxiv.1408.2144

19 pages

arxiv created 2014/08/09 · arxiv updated 2014/08/12

Abstract

For the strictly positive case (the suboptimal case) the maximum entropy solution X to the Leech problem G(z)X(z)=K(z) and ‖X‖_∞=sup_{|z|≤ 1}‖X(z)‖≤ 1, with G and K stable rational matrix functions, is proved to be a stable rational matrix function. An explicit state space realization for X is given, and ‖X‖_∞ turns out to be strictly less than one. The matrices involved in this realization are computed from the matrices appearing in a state space realization of the data functions G and K. A formula for the entropy of X is also given.

Related

• The maximum entropy state
• Matrix Completion by the Principle of Parsimony
• Optimizing entropy relative to a channel or a subalgebra
• Entropy and optimal decompositions of states relative to a maximal commutative subalgebra
• Computation of the von Neumann entropy of large matrices via trace estimators and rational Krylov methods