Browsing by Author "Li, Tie-Xiang"

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A structure-preserving doubling algorithm for quadratic eigenvalue problems arising from time-delay systems
(2010-02-15)
Li, Tie-Xiang
;
Chu, Eric King-wah
;
Lin, Wen-Wei
;
應用數學系
;
Department of Applied Mathematics
We propose a structure-preserving doubling algorithm for a quadratic eigenvalue problem arising from the stability analysis of time-delay systems. We are particularly interested in the eigenvalues oil the unit circle, which are difficult to estimate. The convergence and backward error of the algorithm are analyzed and three numerical examples are presented. Our experience shows that Our algorithm is efficient in comparison to the few existing approaches for small to medium size problems. (C) 2009 Elsevier B.V. All rights reserved.
Solution of a nonsymmetric algebraic Riccati equation from a two-dimensional transport model
(2011-01-01)
Li, Tie-Xiang
;
Chu, Eric King-wah
;
Juang, Jong
;
Lin, Wen-Wei
;
電子物理學系
For the steady-state solution of an integral-differential equation from a two-dimensional model in transport theory, we shall derive and study a nonsymmetric algebraic Riccati equation B(-) - XF(-) - F(+)X + XB(+)X = 0, where F(+/-) equivalent to I - (s) over cap PD(+/-), B(-) equivalent to (b) over capl + (s) over capP)D(-))D(-) and B(+) equivalent to (b) over capl + (s) over capP)D(+))D(+) with a nonnegative matrix P, positive diagonal matrices D, and nonnegative parameters f, (b) over cap equivalent to(1 - f) and (s) over cap equivalent to (1 - f). We prove the existence of the minimal nonnegative solution X* under the physically reasonable assumption f + b + s parallel to P(D(+) + D-)parallel to(infinity) < 1, and study its numerical computation by fixed-point iteration, Newton's method and doubling. We shall also study several special cases; e.g. when = 0 and P is low-ranked, then X* = <(s)over cap>/2 UV is low-ranked and can be computed using more efficient iterative processes in U and V. Numerical examples will be given to illustrate our theoretical results. (C) 2010 Elsevier Inc. All rights reserved.