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Explicit Solutions for a Riccati Equation from Transport Theory

Mehrmann, Volker
; 
Xu, Hongguo
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Abstract
We derive formulas for the minimal positive solution of a particular nonsymmetric 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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This is the published version, also available here: http://dx.doi.org/10.1137/070708743.
Date
2008-10-16
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Society for Industrial and Applied Mathematics
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Mathematics Scholarly Works
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XuHongguo_SIAMJMAA_30(4)1339.pdf
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Keywords
nonsymmetric Riccati equation, secular equation, eigenvalues, minimal positive solution, Cauchy matrix, transport theory, quadrature formula
Citation
Mehrmann, Volker & Xu, Hongguo. "Explicit Solutions for a Riccati Equation from Transport Theory." (2008) SIAM. J. Matrix Anal. & Appl., 30(4), 1339–1357. (19 pages). http://dx.doi.org/10.1137/070708743.
URI
https://hdl.handle.net/1808/17353
DOI
10.1137/070708743
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