Title: SOLVING LARGE-SCALE NONSYMMETRIC ALGEBRAIC RICCATI EQUATIONS BY DOUBLING
Authors: Li, Tiexiang
Chu, Eric King-Wah
Kuo, Yueh-Cheng
Lin, Wen-Wei
應用數學系
Department of Applied Mathematics
Keywords: doubling algorithm;M-matrix;nonsymmetric algebraic Riccati equation;numerically low-ranked solution
Issue Date: 2013
Abstract: We consider the solution of the large-scale nonsymmetric algebraic Riccati equation XCX - XD - AX + B = 0, with M = [D, -C; -B, A] is an element of R(n perpendicular to+n2)x(n perpendicular to +n2) being a nonsingular M-matrix. In addition, A and D are sparselike, with the products A(-1)u, A(-T)u, D(-1)v, and D(-T)v computable in O(n) complexity (with n = max{n(1), n(2)}), for some vectors u and v, and B, C are low ranked. The structure-preserving doubling algorithms (SDA) by Guo, Lin, and Xu [Numer. Math., 103 (2006), pp. 392-412] is adapted, with the appropriate applications of the Sherman-Morrison-Woodbury formula and the sparse-plus-low-rank representations of various iterates. The resulting large-scale doubling algorithm has an O(n) computational complexity and memory requirement per iteration and converges essentially quadratically. A detailed error analysis, on the effects of truncation of iterates with an explicit forward error bound for the approximate solution from the SDA, and some numerical results will be presented.
URI: http://hdl.handle.net/11536/22820
http://dx.doi.org/10.1137/110858070
ISSN: 0895-4798
DOI: 10.1137/110858070
Journal: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Volume: 34
Issue: 3
Begin Page: 1129
End Page: 1147
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