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Solving time-invariant differential matrix Riccati equations using GPGPU computing

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Solving time-invariant differential matrix Riccati equations using GPGPU computing

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Peinado Pinilla, J.; Alonso-Jordá, P.; Ibáñez González, JJ.; Hernández García, V.; Do Carmo Boratto, M. (2014). Solving time-invariant differential matrix Riccati equations using GPGPU computing. Journal of Supercomputing. 70(2):623-636. doi:10.1007/s11227-014-1111-3

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/49225

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Title: Solving time-invariant differential matrix Riccati equations using GPGPU computing
Author:
UPV Unit: Universitat Politècnica de València. Departamento de Sistemas Informáticos y Computación - Departament de Sistemes Informàtics i Computació
Universitat Politècnica de València. Instituto de Instrumentación para Imagen Molecular - Institut d'Instrumentació per a Imatge Molecular
Issued date:
Abstract:
Differential matrix Riccati equations (DMREs) enable to model many physical systems appearing in different branches of science, in some cases, involving very large problem sizes. In this paper, we propose an adaptive ...[+]
Subjects: Differential matrix Riccati equation (DMRE) , Ordinary differential equation (ODE) , Piecewise-linearized method , Padé approximants , GPGPU
Copyrigths: Cerrado
Source:
Journal of Supercomputing. (issn: 0920-8542 )
DOI: 10.1007/s11227-014-1111-3
Publisher:
Springer Verlag (Germany)
Publisher version: http://link.springer.com/article/10.1007%2Fs11227-014-1111-3
Type: Artículo

References

Anderson E et al (1994) LAPACK users’ guide. SIAM, Philadelphia

Arias E, Hernández V, Ibáñez J, Peinado J (2007) A fixed point-based BDF method for solving Riccati equations. Appl Math Comput 188(2):1319–1333

Benner P, Mena H (2004) BDF methods for large-scale differential Riccati equations. In: 16th International symposium on mathematical theory of network and systems (MTNS2004), Katholieke Universiteit Leuven, Belgium [+]
Anderson E et al (1994) LAPACK users’ guide. SIAM, Philadelphia

Arias E, Hernández V, Ibáñez J, Peinado J (2007) A fixed point-based BDF method for solving Riccati equations. Appl Math Comput 188(2):1319–1333

Benner P, Mena H (2004) BDF methods for large-scale differential Riccati equations. In: 16th International symposium on mathematical theory of network and systems (MTNS2004), Katholieke Universiteit Leuven, Belgium

Benner P, Mena H (2013) Rosenbrock methods for solving Riccati differential equations. IEEE Trans Autom Control 58(11):2950–2956

Chandrasekhar H (1976) Generalized Chandrasekhar algorithms: time-varying models. IEEE Trans Autom Control 21:728–732

Chen B, Company R, Jdar L, Rosell MD (2007) Constructing accurate polynomial approximations for nonlinear differential initial value problems. Appl Math Comput 193:523–534

Choi CH (1988) Efficient algorithms for solving stiff matrix-valued Riccati differential equations. PhD thesis, University of California, California

Choi CH (1992) Time-varying Riccati differential equations with known analytic solutions. IEEE Trans Autom Control 37:642–645

Davison EJ, Maki MC (1973) The numerical solution of the matrix Riccati differential equation. IEEE Trans Autom Control 18(1):71–73

Defez E, Hervs A, Soler L, Tung MM (2007) Numerical solutions of matrix differential models using cubic matrix splines II. Math Comput Model 46:657–669

Dieci L (1992) Numerical integration of the differential Riccati equation and some related issues. SIAM J Numer Anal 29(3):781–815

EM Photonics (2011) CULATOOLS, R12 edn

Hernández V, Ibáñez J, Arias E, Peinado J (2008) A GMRES-based BDF method for solving differential Riccati equations. Appl. Math. Comput. 196(2):613–626

Horn RA, Johnson CR (1991) Topics in matrix analysis. Cambridge University Press, London

Ibáñez J, Hernández V (2010) Solving differential matrix Riccati equations by a piecewise-linearized method based on the conmutant equation. Comput Phys Commun 180:2103–2114

Ibáñez J, Hernández V (2011) Solving differential matrix Riccati equations by a piecewise-linearized method based on diagonal Padé approximants. Comput Phys Commun 182:669–678

Ibáñez J, Hernández V, Arias E, Ruiz P (2009) Solving initial value problems for ordinary differential equations by two approaches: BDF and piecewise-linearized methods. Comput Phys Commun 180(5):712–723

Kenney CS, Leipnik RB (1985) Numerical integration of the differential matrix Riccati equation. IEEE Trans Autom Control 30:962–970

Li R-C (2000) Unconventional reflexive numerical methods for matrix differential Riccati. In: Technical report 2000-36, Department of Mathematics, University of Kentucky, Lexington

MathWorks (2013) MATLAB MEX files. http://www.mathworks.es/es/help/matlab/create-mex-files.html . Accessed June 2013

MathWorks (2013) MATLAB parallel computing toolbox. http://www.mathworks.es/products/parallel-computing . Accessed June 2013

Meyer GH (1973) Initial value methods for boundary value problems. Academic Press, New York

NVIDIA Corporation (2013) CUBLAS library. http://docs.nvidia.com/cuda/cublas/ . Accessed June 2013

NVIDIA Corporation (2013) CUDA C programming guide.  http://docs.nvidia.com/cuda/cuda-c-programming-guide . Accessed June 2013

Ramos JI, García CM (1997) Piecewise-linearized methods for initial-value problems. Appl Math Comput 82:273–302

Rand DW, Winternitz P (1984) Nonlinear superposition principles: a new numerical method for solving matrix Riccati equations. Comput Phys Commun 33:305–328

Sanz-Serna JM (1992) Symplectic integrators for Hamiltonian problems: an overview. Acta Numer 1:243–286

Sastre J, Ibez J, Defez E, Ruiz P (2011) Accurate matrix exponential computation to solve coupled differential models in engineering. Math Comput Model 54:1835–1840

Sorine M, Winternitz P (1985) Superposition laws for the solution of differential Riccati equations. IEEE Trans Autom Control 30:266–272

Vaughan DR (1969) A negative exponential solution for the matrix Riccati equation. IEEE Trans Autom Control 14(1):72–75

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