A factored variant of the Newton iteration for the solution of algebraic Riccati equations via the matrix sign function
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http://dx.doi.org/ 10.1007/s11075-013-9739-2 |
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Title
A factored variant of the Newton iteration for the solution of algebraic Riccati equations via the matrix sign functionDate
2013Publisher
SpringerISSN
1017-1398; 1572-9265Type
info:eu-repo/semantics/articlePublisher version
http://download.springer.com/static/pdf/621/art%253A10.1007%252Fs11075-013-9739- ...Subject
Abstract
In this paper we introduce a variant of the Newton iteration for the matrix sign function that results in an efficient numerical solver for a certain class of algebraic Riccati equations (AREs). In particular, when ... [+]
In this paper we introduce a variant of the Newton iteration for the matrix sign function that results in an efficient numerical solver for a certain class of algebraic Riccati equations (AREs). In particular, when the Hamiltonian matrix associated with the ARE can be composed as [ACTCBBT−AT] , with B and CT having a much larger number of rows than columns, the new algorithm exploits the special structure of the off-diagonal blocks to yield an alternative factored Newton iteration which reduces the cost per iteration by a factor of up to 8 (16 in case A is symmetric negative definite) w.r.t. the conventional iterative scheme. Experiments with a large collection of benchmark examples show that the factored iteration attains numerical accuracy similar to that of the conventional Newton iteration as well as the structure-preserving doubling algorithm. High-performance implementations of these methods, making heavy use of LAPACK linked to a multi-threaded implementation of BLAS, demonstrate the clear advantage of the new iteration on a 48-core AMD-based platform. [-]
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Numerical Algorithms, 2013, JulyRights
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