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Explicit Solutions for a Riccati Equation from Transport Theory

Please always quote using this URN:urn:nbn:de:0296-matheon-4283
  • We derive formulas for the minimal positive solution of a particular non-symmetric Riccati equation arising in transport theory. The formulas are based on the eigenvalues of an associated matrix. We use the formulas to explore some new properties of the minimal positive solution and to derive fast and highly accurate numerical methods. Some numerical tests demonstrate the properties of the new methods.

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Metadaten
Author:Volker Mehrmann, Hongguo Xu
URN:urn:nbn:de:0296-matheon-4283
Referee:Andreas Griewank
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2007/06/12
Release Date:2007/11/20
Tag:
Institute:Technische Universität Berlin
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A24 Matrix equations and identities
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
65-XX NUMERICAL ANALYSIS / 65Hxx Nonlinear algebraic or transcendental equations / 65H05 Single equations
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) / 82C70 Transport processes
Preprint Number:418
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