- -

Factorized solution of generalized stable Sylvester equations using many-core GPU accelerators

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Factorized solution of generalized stable Sylvester equations using many-core GPU accelerators

Mostrar el registro completo del ítem

Benner, P.; Dufrechou, E.; Ezzatti, P.; Gallardo, R.; Quintana-Ortí, ES. (2021). Factorized solution of generalized stable Sylvester equations using many-core GPU accelerators. The Journal of Supercomputing (Online). 77(9):10152-19164. https://doi.org/10.1007/s11227-021-03658-y

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/188824

Ficheros en el ítem

Metadatos del ítem

Título: Factorized solution of generalized stable Sylvester equations using many-core GPU accelerators
Autor: Benner, Peter Dufrechou, Ernesto Ezzatti, Pablo Gallardo, Rodrigo Quintana-Ortí, Enrique S.
Entidad UPV: Universitat Politècnica de València. Departamento de Informática de Sistemas y Computadores - Departament d'Informàtica de Sistemes i Computadors
Fecha difusión:
Resumen:
[EN] We investigate the factorized solution of generalized stable Sylvester equations such as those arising in model reduction, image restoration, and observer design. Our algorithms, based on the matrix sign function, ...[+]
Palabras clave: Sylvester equation , Matrix sign function , Newton iteration , GPUs
Derechos de uso: Reserva de todos los derechos
Fuente:
The Journal of Supercomputing (Online). (eissn: 1573-0484 )
DOI: 10.1007/s11227-021-03658-y
Editorial:
Springer-Verlag
Versión del editor: https://doi.org/10.1007/s11227-021-03658-y
Agradecimientos:
We acknowledge support of the ANII - MPG Independent Research Group: "Efficient Hetergenous Computing" at UdelaR, a partner group of the Max Planck Institute in Magdeburg.
Tipo: Artículo

References

Benner P, Quintana-Ortí ES, Quintana-Ortí G (2005) Solving stable Sylvester equations via rational iterative schemes. J Sci Comput 28(1):51–83

Aldhaheri R (1991) Model order reduction via real Schur-form decomposition. Int J Control 53(3):709–716

Benner P, Himpe C (2019) Cross-Gramian-based dominant subspaces. Adv Comput Math 45(5):2533–2553 [+]
Benner P, Quintana-Ortí ES, Quintana-Ortí G (2005) Solving stable Sylvester equations via rational iterative schemes. J Sci Comput 28(1):51–83

Aldhaheri R (1991) Model order reduction via real Schur-form decomposition. Int J Control 53(3):709–716

Benner P, Himpe C (2019) Cross-Gramian-based dominant subspaces. Adv Comput Math 45(5):2533–2553

Fernando K, Nicholson H (1984) On a fundamental property of the cross-Gramian matrix. IEEE Trans Circuits Syst CAS-31(5):504–505

Himpe C, Ohlberger M (2014) Cross-Gramian based combined state and parameter reduction for large-scale control systems. Math. Probl. Eng. 2014:843869

Calvetti D, Reichel L (1996) Application of ADI iterative methods to the restoration of noisy images. SIAM J Matrix Anal Appl 17:165–186

Datta B (2003) Numerical methods for linear control systems design and analysis. Elsevier Press, Amsterdam

Grasedyck L (2004) Existence of a low rank or $$H$$-matrix approximant to the solution of a Sylvester equation. Numer Lin Alg Appl 11:371–389

Benner P (2004) “Factorized solution of Sylvester equations with applications in control,” in Proc. Intl. Symp. Math. Theory Networks and Syst, MTNS, p 2004

Köhler M, Saak J (2016) On GPU acceleration of common solvers for (quasi-) triangular generalized Lyapunov equations. Par Comp 57:212–221

Köhler M , Saak J (2016) On BLAS level-3 implementations of common solvers for (quasi-) triangular generalized Lyapunov equations. ACM Trans Math Softw 43(1), art. no. 3

Schwarz A, Mikkelsen C (2019) Robust task-parallel solution of the triangular Sylvester equation. In: International Conference on Parallel Processing and Applied Mathematics. Springer, Cham

Xiao M, Lv Q, Xing Z, Zhang Y (2017) A parallel two-stage iteration method for solving continuous Sylvester equations. Algorithms 10(3), art. no. 95

Benner P, Ezzatti P, Mena H, Quintana-Ortí ES, Remón A (2013) Solving matrix equations on multi-core and many-core architectures. Algorithms 6(4):857–870

Dufrechu E, Ezzatti P, Quintana-Ortí ES, Remón A (2013) Accelerating the Lyapack library using GPUs. J Supercomput 65(3):1114–1124. https://doi.org/10.1007/s11227-013-0889-8

Bartels R, Stewart G (1972) Solution of the matrix equation $${AX}+{XB}={C}$$: Algorithm 432. Commun ACM 15:820–826

Enright W (1978) Improving the efficiency of matrix operations in the numerical solution of stiff ordinary differential equations. ACM Trans Math Softw 4:127–136

Golub GH, Nash S, Van Loan C F (1979)A Hessenberg–Schur method for the problem $$AX+XB=C$$. IEEE Trans Aut Control AC-24:909–913

Roberts J (1980) Linear model reduction and solution of the algebraic Riccati equation by use of the sign function. Int J Control 32:677–687 (Reprint Tech. Report No. TR-13, CUED/B-Control, Cambridge Univ., Engineering Dept., 1971)

Benner P, Quintana-Ortí ES (1999) Solving stable generalized Lyapunov equations with the matrix sign function. Numer Algor 20(1):75–100

Benner P, Claver J, Quintana-Ortí E (1999) Parallel distributed solvers for large stable generalized Lyapunov equations. Parallel Proc Lett 9(1):147–158

Byers R (1987) Solving the algebraic Riccati equation with the matrix sign function. Linear Algebra Appl 85:267–279

Higham N (1986) Computing the polar decomposition-with applications. SIAM J Sci Statist Comput 7:1160–1174

Chan T (1987) Rank revealing QR factorizations. Linear Algebra Appl 88(89):67–82

Abels J, Benner P (1999) CAREX—a collection of benchmark examples for continuous-time algebraic Riccati equations (version 2.0).’ SLICOT Working Note 1999-14, Available from http://www.slicot.org

Slowik M, Benner P, Sima V (2007) Evaluation of the linear matrix equation solvers in SLICOT. J Numer Anal Ind Appl Math 2(1–2):11–34

Aliaga JI, Badia RM, Barreda M, Bollhöfer M, Dufrechou E, Ezzatti P, Quintana-Ortí ES (2016) Exploiting task and data parallelism in ILUPACK’s preconditioned CG solver on NUMA architectures and many-core accelerators. Parallel Comp 54:97–107

[-]

recommendations

 

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro completo del ítem