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A GMRES-based BDF method for solving differential Riccati equations

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A GMRES-based BDF method for solving differential Riccati equations

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dc.contributor.author Hernández García, Vicente es_ES
dc.contributor.author Ibáñez González, Jacinto Javier es_ES
dc.contributor.author Peinado Pinilla, Jesús es_ES
dc.contributor.author Arias, E. es_ES
dc.date.accessioned 2014-11-17T10:20:50Z
dc.date.available 2014-11-17T10:20:50Z
dc.date.issued 2008-03-01
dc.identifier.issn 0096-3003
dc.identifier.uri http://hdl.handle.net/10251/44261
dc.description.abstract Differential Riccati equations play a fundamental role in control theory, for example, optimal control, filtering and estimation, decoupling and order reduction, etc. The most popular codes to solve stiff differential Riccati equations use backward differentiation formula (BDF) methods. In this paper, a new approach to solve differential Riccati equations by means of a BDF method is described. In each step of these methods an algebraic Riccati equation is obtained, which is solved by means of Newton’s method. In the standard approach, this system is transformed into a Sylvester equation, which could be solved by means of the well-known Bartels–Stewart method. In our code, we obtain a system of linear equations, defined from a Kronecker product of matrices related to coefficient matrices of the differential Riccati equation, that is solved by means of the iterative generalized minimum residual (GMRES) method. We have also implemented an efficient matrix–vector product in order to reduce the computational and storage cost of the GMRES method. The above approach has been applied in the development of an algorithm to solve differential Riccati equations. The accuracy and efficiency of this algorithm has been compared with the BDF algorithm that uses the Bartels–Stewart method. Experimental results show the advantages of the new algorithm. es_ES
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation.ispartof Applied Mathematics and Computation es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Differential Riccati equations es_ES
dc.subject BDF methods es_ES
dc.subject GMRES methods es_ES
dc.subject Algebraic Riccati Equation es_ES
dc.subject.classification CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL es_ES
dc.subject.classification LENGUAJES Y SISTEMAS INFORMATICOS es_ES
dc.title A GMRES-based BDF method for solving differential Riccati equations es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/J.Amc.2007.06.021
dc.rights.accessRights Cerrado es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Sistemas Informáticos y Computación - Departament de Sistemes Informàtics i Computació es_ES
dc.description.bibliographicCitation Hernández García, V.; Ibáñez González, JJ.; Peinado Pinilla, J.; Arias, E. (2008). A GMRES-based BDF method for solving differential Riccati equations. Applied Mathematics and Computation. 196(2):613-626. doi:10.1016/J.Amc.2007.06.021 es_ES
dc.description.accrualMethod Senia es_ES
dc.relation.publisherversion http://dx.doi.org/10.1016/j.amc.2007.06.021 es_ES
dc.description.upvformatpinicio 613 es_ES
dc.description.upvformatpfin 626 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 196 es_ES
dc.description.issue 2 es_ES
dc.relation.senia 33803


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