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A factored variant of the Newton iteration for the solution of algebraic Riccati equations via the matrix sign function
dc.contributor.author | Benner, Peter | |
dc.contributor.author | Ezzatti, Pablo | |
dc.contributor.author | Quintana-Orti, Enrique S. | |
dc.contributor.author | Remón Gómez, Alfredo | |
dc.date.accessioned | 2014-05-23T14:02:20Z | |
dc.date.available | 2014-05-23T14:02:20Z | |
dc.date.issued | 2013 | |
dc.identifier.issn | 1017-1398 | |
dc.identifier.issn | 1572-9265 | |
dc.identifier.uri | http://hdl.handle.net/10234/93405 | |
dc.description.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 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. | ca_CA |
dc.format.extent | 15 p. | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Springer | ca_CA |
dc.relation.isPartOf | Numerical Algorithms, 2013, July | ca_CA |
dc.rights | © Springer Science+Business Media New York 2013. "The final publication is available at link. Springer.com" | ca_CA |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | * |
dc.subject | Algebraic Riccati equations | ca_CA |
dc.subject | Matrix sign function | ca_CA |
dc.subject | Newton iteration | ca_CA |
dc.subject | Multi-core processors | ca_CA |
dc.title | A factored variant of the Newton iteration for the solution of algebraic Riccati equations via the matrix sign function | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | http://dx.doi.org/ 10.1007/s11075-013-9739-2 | |
dc.rights.accessRights | info:eu-repo/semantics/restrictedAccess | ca_CA |
dc.relation.publisherVersion | http://download.springer.com/static/pdf/621/art%253A10.1007%252Fs11075-013-9739-2.pdf?auth66=1401026296_b49567a966f8f3e1817df14bad5c885f&ext=.pdf | ca_CA |
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