Solving large-scale nonsymmetric algebraic Riccati equations by doubling (Q2866228)
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scientific article; zbMATH DE number 6238079
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solving large-scale nonsymmetric algebraic Riccati equations by doubling |
scientific article; zbMATH DE number 6238079 |
Statements
13 December 2013
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doubling algorithm
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M-matrix
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nonsymmetric algebraic Riccati equation
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numerically low-rank solution
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convergence
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Sherman-Morrison-Woodbury formula
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0.94599956
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0.94048697
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0.93806255
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0.93413174
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0.9244456
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0.9243462
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0.92166436
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Solving large-scale nonsymmetric algebraic Riccati equations by doubling (English)
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The authors consider the solution of the large-scale nonsymmetric Riccati matrix equation \(XCX-XD-AX+B=0\), with \(M=[D,-C,-B,A]\) being a nonsingular M-matrix, \(A\) and \(D\) being sparselike, and \(B\) and \(C\) low ranked. By adapting the structure-preserving doubling algorithm (SDA) by \textit{X.-X. Guo} et al. [Numer. Math. 103, No. 3, 393--412 (2006; Zbl 1097.65055)], with the appropriate applications of the Sherman-Morrison-Woodbury formula and the sparse-plus-low-rank representations of various iterates, a new SDA algorithm is presented. The new algorithm has low computational complexity and memory requirement and converges essentially quadratically.
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