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dc.contributor.authorLi, Tiexiangen_US
dc.contributor.authorChu, Eric King-Wahen_US
dc.contributor.authorKuo, Yueh-Chengen_US
dc.contributor.authorLin, Wen-Weien_US
dc.date.accessioned2014-12-08T15:32:37Z-
dc.date.available2014-12-08T15:32:37Z-
dc.date.issued2013en_US
dc.identifier.issn0895-4798en_US
dc.identifier.urihttp://hdl.handle.net/11536/22820-
dc.identifier.urihttp://dx.doi.org/10.1137/110858070en_US
dc.description.abstractWe 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.en_US
dc.language.isoen_USen_US
dc.subjectdoubling algorithmen_US
dc.subjectM-matrixen_US
dc.subjectnonsymmetric algebraic Riccati equationen_US
dc.subjectnumerically low-ranked solutionen_US
dc.titleSOLVING LARGE-SCALE NONSYMMETRIC ALGEBRAIC RICCATI EQUATIONS BY DOUBLINGen_US
dc.typeArticleen_US
dc.identifier.doi10.1137/110858070en_US
dc.identifier.journalSIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONSen_US
dc.citation.volume34en_US
dc.citation.issue3en_US
dc.citation.spage1129en_US
dc.citation.epage1147en_US
dc.contributor.department應用數學系zh_TW
dc.contributor.departmentDepartment of Applied Mathematicsen_US
dc.identifier.wosnumberWOS:000325092700014-
dc.citation.woscount2-
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