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http://dx.doi.org/10.12941/jksiam.2016.20.225

AN OPTIMIZATION APPROACH FOR COMPUTING A SPARSE MONO-CYCLIC POSITIVE REPRESENTATION  

KIM, KYUNGSUP (DEPARTMENT OF COMPUTER ENGINEERING, CHUNGNAM NATIONAL UNIVERSITY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.20, no.3, 2016 , pp. 225-242 More about this Journal
Abstract
The phase-type representation is strongly connected with the positive realization in positive system. We attempt to transform phase-type representation into sparse mono-cyclic positive representation with as low order as possible. Because equivalent positive representations of a given phase-type distribution are non-unique, it is important to find a simple sparse positive representation with lower order that leads to more effective use in applications. A Hypo-Feedback-Coxian Block (HFCB) representation is a good candidate for a simple sparse representation. Our objective is to find an HFCB representation with possibly lower order, including all the eigenvalues of the original generator. We introduce an efficient nonlinear optimization method for computing an HFCB representation from a given phase-type representation. We discuss numerical problems encountered when finding efficiently a stable solution of the nonlinear constrained optimization problem. Numerical simulations are performed to show the effectiveness of the proposed algorithm.
Keywords
Phase-type representation; Hypo-feedback-Coxian block; Constrained nonlinear optimization; Positive realization; Positive system;
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