메뉴 건너뛰기




Volumn 29, Issue 11-12 SPEC.ISS., 2003, Pages 1701-1722

State-space truncation methods for parallel model reduction of large-scale systems

Author keywords

Algebraic Riccati equations; Linear matrix equations; Model reduction; Parallel linear algebra; Sign function method; State space truncation

Indexed keywords

ALGORITHMS; ITERATIVE METHODS; LINEAR ALGEBRA; MATHEMATICAL MODELS; PARALLEL PROCESSING SYSTEMS; RICCATI EQUATIONS;

EID: 0242406989     PISSN: 01678191     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.parco.2003.05.013     Document Type: Article
Times cited : (43)

References (50)
  • 2
    • 0031215987 scopus 로고    scopus 로고
    • The spectral decomposition of nonsymmetric matrices on distributed memory parallel computers
    • Bai Z., Demmel J., Dongarra J., Petitet A., Robinson H., Stanley K. The spectral decomposition of nonsymmetric matrices on distributed memory parallel computers. SIAM J. Sci. Comput. 18:1997;1446-1461.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 1446-1461
    • Bai, Z.1    Demmel, J.2    Dongarra, J.3    Petitet, A.4    Robinson, H.5    Stanley, K.6
  • 3
    • 84949104596 scopus 로고    scopus 로고
    • Numerical solution of special algebraic Riccati equations via an exact line search method
    • Paper 786, BELWARE Information Technology, Waterloo, Belgium
    • P. Benner, Numerical solution of special algebraic Riccati equations via an exact line search method, in: Proc. European Control Conf. ECC 97 (CD-ROM), Paper 786, BELWARE Information Technology, Waterloo, Belgium, 1997.
    • (1997) Proc. European Control Conf. ECC 97 (CD-ROM)
    • Benner, P.1
  • 4
    • 0343389560 scopus 로고    scopus 로고
    • Solving algebraic Riccati equations on parallel computers using Newton's method with exact line search
    • Benner P., Byers R., Quintana-Ortí E.S., Quintana-Ortí G. Solving algebraic Riccati equations on parallel computers using Newton's method with exact line search. Parallel Comput. 26(10):2000;1345-1368.
    • (2000) Parallel Comput. , vol.26 , Issue.10 , pp. 1345-1368
    • Benner, P.1    Byers, R.2    Quintana-Ortí, E.S.3    Quintana-Ortí, G.4
  • 5
    • 0033412866 scopus 로고    scopus 로고
    • Solving stable generalized Lyapunov equations with the matrix sign function
    • Benner P., Quintana-Ortí E.S. Solving stable generalized Lyapunov equations with the matrix sign function. Numer. Algorithms. 20(1):1999;75-100.
    • (1999) Numer. Algorithms , vol.20 , Issue.1 , pp. 75-100
    • Benner, P.1    Quintana-Ortí, E.S.2
  • 7
    • 0034549981 scopus 로고    scopus 로고
    • Balanced truncation model reduction of large-scale dense systems on parallel computers
    • Benner P., Quintana-Ortí E.S., Quintana-Ortí G. Balanced truncation model reduction of large-scale dense systems on parallel computers. Math. Comput. Model. Dyn. Syst. 6(4):2000;383-405.
    • (2000) Math. Comput. Model. Dyn. Syst. , vol.6 , Issue.4 , pp. 383-405
    • Benner, P.1    Quintana-Ortí, E.S.2    Quintana-Ortí, G.3
  • 8
    • 0242274060 scopus 로고    scopus 로고
    • Parallel algorithms for model reduction of discrete-time systems
    • Benner P., Quintana-Ortí E.S., Quintana-Ortí G. Parallel algorithms for model reduction of discrete-time systems. Int. J. Syst. Sci. 34(5/15):2003;319-333.
    • (2003) Int. J. Syst. Sci. , vol.34 , Issue.5-15 , pp. 319-333
    • Benner, P.1    Quintana-Ortí, E.S.2    Quintana-Ortí, G.3
  • 10
    • 0242505782 scopus 로고    scopus 로고
    • Experimental evaluation of the parallel model reduction routines in PSLICOT
    • August
    • P. Benner, E.S. Quintana-Ortí, G. Quintana-Ortí, Experimental evaluation of the parallel model reduction routines in PSLICOT, SLICOT Working Note 2002-7, August 2002. Available from 〈 http://www.win.tue.nl/niconet/NIC2/reports.html〉.
    • (2002) SLICOT Working Note , vol.2002 , Issue.7
    • Benner, P.1    Quintana-Ortí, E.S.2    Quintana-Ortí, G.3
  • 11
    • 0242281707 scopus 로고    scopus 로고
    • Numerical solution of discrete stable linear matrix equations on multicomputers
    • Benner P., Quintana-Ortí E.S., Quintana-Ortí G. Numerical solution of discrete stable linear matrix equations on multicomputers. Parallel Algorithms Appl. 17(1):2002;127-146.
    • (2002) Parallel Algorithms Appl. , vol.17 , Issue.1 , pp. 127-146
    • Benner, P.1    Quintana-Ortí, E.S.2    Quintana-Ortí, G.3
  • 13
    • 0242505804 scopus 로고    scopus 로고
    • Pool boiling at high heat fluxes (part I): Local temperature & heat flux fluctuations at the heater surface
    • D. Gorenflo, A. Luke (Eds.), Paderborn, Germany, October
    • M. Buchholz, T. Lüttich, H. Auracher, W. Marquardt, Pool boiling at high heat fluxes (part I): local temperature & heat flux fluctuations at the heater surface, in: D. Gorenflo, A. Luke (Eds.), Proc. Int. Refrig. Conf. Comm. B1, Paderborn, Germany, October 2001.
    • (2001) Proc. Int. Refrig. Conf. Comm. B1
    • Buchholz, M.1    Lüttich, T.2    Auracher, H.3    Marquardt, W.4
  • 14
    • 38249038136 scopus 로고
    • Solving the algebraic Riccati equation with the matrix sign function
    • Byers R. Solving the algebraic Riccati equation with the matrix sign function. Linear Algebra Appl. 85:1987;267-279.
    • (1987) Linear Algebra Appl. , vol.85 , pp. 267-279
    • Byers, R.1
  • 15
    • 0242674368 scopus 로고    scopus 로고
    • A collection of benchmark examples for model reduction of linear time invariant dynamical systems
    • February
    • Y. Chahlaoui, P. Van Dooren, A collection of benchmark examples for model reduction of linear time invariant dynamical systems, SLICOT Working Note 2002-2, February 2002. Available from 〈 http://www.win.tue.nl/niconet/NIC2/reports.html〉.
    • (2002) SLICOT Working Note , vol.2002 , Issue.2
    • Chahlaoui, Y.1    Van Dooren, P.2
  • 17
    • 0021542280 scopus 로고
    • A transformation approach to stochastic model reduction
    • Desai U.B., Pal D. A transformation approach to stochastic model reduction. IEEE Trans. Automat. Control. AC-29:1984;1097-1100.
    • (1984) IEEE Trans. Automat. Control , vol.AC-29 , pp. 1097-1100
    • Desai, U.B.1    Pal, D.2
  • 18
    • 0000658386 scopus 로고    scopus 로고
    • Reduced-order modeling techniques based on Krylov subspaces and their use in circuit simulation
    • B.N. Datta. Boston, MA: Birkhäuser. (Chapter 9)
    • Freund R. Reduced-order modeling techniques based on Krylov subspaces and their use in circuit simulation. Datta B.N. Applied and Computational Control, Signals, and Circuits, vol. 1. 1999;435-498 Birkhäuser, Boston, MA. (Chapter 9).
    • (1999) Applied and Computational Control, Signals, and Circuits , vol.1 , pp. 435-498
    • Freund, R.1
  • 22
    • 0000921740 scopus 로고
    • Balanced stochastic realization
    • Green M. Balanced stochastic realization. Linear Algebra Appl. 98:1988;211-247.
    • (1988) Linear Algebra Appl. , vol.98 , pp. 211-247
    • Green, M.1
  • 23
    • 27544508073 scopus 로고    scopus 로고
    • Model reduction of state space systems via an implicitly restarted Lanczos method
    • Grimme E.J., Sorensen D.C., Van Dooren P. Model reduction of state space systems via an implicitly restarted Lanczos method. Numer. Algorithms. 12:1996;1-31.
    • (1996) Numer. Algorithms , vol.12 , pp. 1-31
    • Grimme, E.J.1    Sorensen, D.C.2    Van Dooren, P.3
  • 24
    • 0034442126 scopus 로고    scopus 로고
    • Parallel spectral division using the matrix sign function for the generalized eigenproblem
    • Huss S., Quintana-Ortí E.S., Sun X., Wu J. Parallel spectral division using the matrix sign function for the generalized eigenproblem. Int. J. High Speed Comput. 11(1):2000;1-14.
    • (2000) Int. J. High Speed Comput. , vol.11 , Issue.1 , pp. 1-14
    • Huss, S.1    Quintana-Ortí, E.S.2    Sun, X.3    Wu, J.4
  • 26
    • 84914965022 scopus 로고
    • On an iterative technique for Riccati equation computations
    • Kleinman D.L. On an iterative technique for Riccati equation computations. IEEE Trans. Automat. Control. AC-13:1968;114-115.
    • (1968) IEEE Trans. Automat. Control , vol.AC-13 , pp. 114-115
    • Kleinman, D.L.1
  • 28
    • 0027543772 scopus 로고
    • Construction of square root factor for solution of the Lyapunov matrix equation
    • Larin V.B., Aliev F.A. Construction of square root factor for solution of the Lyapunov matrix equation. Sys. Control Lett. 20:1993;109-112.
    • (1993) Sys. Control Lett. , vol.20 , pp. 109-112
    • Larin, V.B.1    Aliev, F.A.2
  • 29
    • 0023288081 scopus 로고
    • Computation of system balancing transformations and other application of simultaneous diagonalization algorithms
    • Laub A.J., Heath M.T., Paige C.C., Ward R.C. Computation of system balancing transformations and other application of simultaneous diagonalization algorithms. IEEE Trans. Automat. Control. 34:1987;115-122.
    • (1987) IEEE Trans. Automat. Control , vol.34 , pp. 115-122
    • Laub, A.J.1    Heath, M.T.2    Paige, C.C.3    Ward, R.C.4
  • 30
    • 0037287244 scopus 로고    scopus 로고
    • Low rank solution of Lyapunov equations
    • Li J.-R., White J. Low rank solution of Lyapunov equations. SIAM J. Matrix Anal. Appl. 24(1):2002;260-280.
    • (2002) SIAM J. Matrix Anal. Appl. , vol.24 , Issue.1 , pp. 260-280
    • Li, J.-R.1    White, J.2
  • 31
    • 0022769212 scopus 로고
    • Controller reduction via stable factorization and balancing
    • Liu Y., Anderson B.D.O. Controller reduction via stable factorization and balancing. Int. J. Control. 44:1986;507-531.
    • (1986) Int. J. Control , vol.44 , pp. 507-531
    • Liu, Y.1    Anderson, B.D.O.2
  • 32
    • 0019533482 scopus 로고
    • Principal component analysis in linear systems: Controllability, observability, and model reduction
    • Moore B.C. Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE Trans. Automat. Control. AC-26:1981;17-32.
    • (1981) IEEE Trans. Automat. Control , vol.AC-26 , pp. 17-32
    • Moore, B.C.1
  • 36
    • 0000841184 scopus 로고    scopus 로고
    • A BLAS-3 version of the QR factorization with column pivoting
    • Quintana-Ortí G., Sun X., Bischof C.H. A BLAS-3 version of the QR factorization with column pivoting. SIAM J. Sci. Comput. 19:1998;1486-1494.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 1486-1494
    • Quintana-Ortí, G.1    Sun, X.2    Bischof, C.H.3
  • 37
    • 0019069037 scopus 로고
    • Linear model reduction and solution of the algebraic Riccati equation by use of the sign function
    • Roberts J.D. Linear model reduction and solution of the algebraic Riccati equation by use of the sign function. Int. J. Control. 32:1980;677-687. (Reprint of Technical Report No. TR-13, CUED/B-Control, Cambridge University, Engineering Department, 1971).
    • (1980) Int. J. Control , vol.32 , pp. 677-687
    • Roberts, J.D.1
  • 38
    • 0019069037 scopus 로고
    • CUED/B-Control, Cambridge University, Engineering Department
    • Roberts J.D. Linear model reduction and solution of the algebraic Riccati equation by use of the sign function. Int. J. Control. 32:1980;677-687. (Reprint of Technical Report No. TR-13, CUED/B-Control, Cambridge University, Engineering Department, 1971).
    • (1971) Technical Report No. TR-13 , vol.TR-13
  • 39
    • 0024123198 scopus 로고
    • Model reduction for robust control: A Schur relative error method
    • Safonov M.G., Chiang R.Y. Model reduction for robust control: a Schur relative error method. Int. J. Adapt. Cont. Sign. Proc. 2:1988;259-272.
    • (1988) Int. J. Adapt. Cont. Sign. Proc. , vol.2 , pp. 259-272
    • Safonov, M.G.1    Chiang, R.Y.2
  • 40
    • 0024700032 scopus 로고
    • A Schur method for balanced-truncation model reduction
    • Safonov M.G., Chiang R.Y. A Schur method for balanced-truncation model reduction. IEEE Trans. Automat. Control. AC-34:1989;729-733.
    • (1989) IEEE Trans. Automat. Control , vol.AC-34 , pp. 729-733
    • Safonov, M.G.1    Chiang, R.Y.2
  • 42
    • 0023439931 scopus 로고
    • Truncated balanced realization of a stable non-minimal state-space system
    • Tombs M.S., Postlethwaite I. Truncated balanced realization of a stable non-minimal state-space system. Int. J. Control. 46(4):1987;1319-1330.
    • (1987) Int. J. Control , vol.46 , Issue.4 , pp. 1319-1330
    • Tombs, M.S.1    Postlethwaite, I.2
  • 44
    • 0026396849 scopus 로고
    • Balancing-free square-root algorithm for computing singular perturbation approximations
    • Brighton, UK
    • A. Varga, Balancing-free square-root algorithm for computing singular perturbation approximations, in: Proc. 30th IEEE Conf. Dec. Control, Brighton, UK, 1991, pp. 1062-1065.
    • (1991) Proc. 30th IEEE Conf. Dec. Control , pp. 1062-1065
    • Varga, A.1
  • 46
    • 0242590460 scopus 로고
    • On computing high accuracy solutions of a class of Riccati equations
    • Varga A. On computing high accuracy solutions of a class of Riccati equations. Control - Theory Adv. Technol. 10(4):1995;2005-2016.
    • (1995) Control - Theory Adv. Technol. , vol.10 , Issue.4 , pp. 2005-2016
    • Varga, A.1
  • 47
    • 0242590454 scopus 로고    scopus 로고
    • Task II.B.1 - Selection of software for controller reduction
    • The Working Group on Software (WGS), December
    • A. Varga, Task II.B.1 - selection of software for controller reduction, SLICOT Working Note 1999-18, The Working Group on Software (WGS), December 1999. Available from 〈http://www.win.tue.nl/niconet/NIC2/reports.html〉.
    • (1999) SLICOT Working Note , vol.1999 , Issue.18
    • Varga, A.1
  • 48
    • 0008296147 scopus 로고    scopus 로고
    • Model reduction software in the SLICOT library
    • Applied and Computational Control, Signals, and Circuits, B.N. Datta. Boston, MA: Kluwer Academic Publishers
    • Varga A. Model reduction software in the SLICOT library. Datta B.N. Applied and Computational Control, Signals, and Circuits. The Kluwer International Series in Engineering and Computer Science. vol. 629:2001;239-282 Kluwer Academic Publishers, Boston, MA.
    • (2001) The Kluwer International Series in Engineering and Computer Science , vol.629 , pp. 239-282
    • Varga, A.1
  • 49
    • 0004843006 scopus 로고
    • A new square-root balancing-free stochastic truncation model reduction algorithm
    • Sydney, Australia
    • A. Varga, K.H. Fasol, A new square-root balancing-free stochastic truncation model reduction algorithm, in: Prepr. 12th IFAC World Congress, vol. 7, Sydney, Australia, 1993, pp. 153-156.
    • (1993) Prepr. 12th IFAC World Congress , vol.7 , pp. 153-156
    • Varga, A.1    Fasol, K.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.