Low-rank approximation to the solution of a nonsymmetric algebraic Riccati equation from transport theory

Chang-Yi Weng, Hung-Yuan Fan, King-Wah Eric Chu

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12 Citations (Scopus)

Abstract

We consider the solution of the large-scale nonsymmetric algebraic Riccati equation XCX - XD - AX + B = 0 from transport theory (Juang 1995), with M equivalent to [D, -C; -B, A] is an element of R(2nx2n) being a nonsingular M-matrix. In addition, A, D are rank-1 updates of diagonal matrices, with the products A(-1)u, A(-T)u, D(-1) v and D(-T) v computable in O(n) complexity, for some vectors u and v, and B, C are rank 1. The structure-preserving doubling algorithm by Guo et al. (2006) 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, as illustrated by the numerical examples.
Original languageEnglish
Pages (from-to)729 - 740
Number of pages12
JournalApplied Mathematics and Computation
Volume219
Issue number2
DOIs
Publication statusPublished - 2012

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