메뉴 건너뛰기




Volumn 57, Issue 8, 2009, Pages 411-419

Model reduction for parametric systems using balanced truncation and interpolation;Modellreduktion für parametrisierte Systeme durch balanciertes Abschneiden und Interpolation

Author keywords

Balanced truncation; Interpolation; Parametric model or derreduction; Sparse grids

Indexed keywords


EID: 70349498397     PISSN: 01782312     EISSN: None     Source Type: Journal    
DOI: 10.1524/auto.2009.0787     Document Type: Article
Times cited : (65)

References (32)
  • 1
    • 84956863380 scopus 로고    scopus 로고
    • Solving large sparse Lyapunov equations on parallel computers
    • B. Monien and R. Feldmann, editors, Euro-Par 2002, Parallel Processing, number in, Springer-Verlag, Berlin, Heidelberg, New York
    • J. Badía, P. Benner, R. Mayo, and E. Quintana-Ortí. Solving large sparse Lyapunov equations on parallel computers. In B. Monien and R. Feldmann, editors, Euro-Par 2002 - Parallel Processing, number 2400 in Lecture Notes in Computer Science, pages 687-690. Springer-Verlag, Berlin, Heidelberg, New York, 2002.
    • (2002) Lecture Notes in Computer Science , vol.2400 , pp. 687-690
    • Badía, J.1    Benner, P.2    Mayo, R.3    Quintana-Ortí, E.4
  • 2
    • 33745323615 scopus 로고    scopus 로고
    • Parallel algorithms for balanced truncation model reduction of sparse systems
    • J. Dongarra, K. Madsen, and J. Wasniewski, editors, Applied Parallel Computing: 7th International Conference, PARA, Lyngby, Denmark, June 20-23, number in, Springer-Verlag, Berlin, Heidelberg, New York, 2006
    • J. Badía, P. Benner, R. Mayo, and E. Quintana-Ortí. Parallel algorithms for balanced truncation model reduction of sparse systems. In J. Dongarra, K. Madsen, and J. Wasniewski, editors, Applied Parallel Computing: 7th International Conference, PARA 2004, Lyngby, Denmark, June 20-23, 2004, number 3732 in Lecture Notes in Computer Science, pages 267-275. Springer-Verlag, Berlin, Heidelberg, New York, 2006.
    • (2004) Lecture Notes in Computer Science , vol.3732 , pp. 267-275
    • Badía, J.1    Benner, P.2    Mayo, R.3    Quintana-Ortí, E.4
  • 3
    • 0034381734 scopus 로고    scopus 로고
    • High dimensional polynomial interpolation on sparse grids
    • V. Barthelmann, E. Novak, and K. Ritter. High dimensional polynomial interpolation on sparse grids. Adv. Comput. Math., 12(4):273-288, 2000.
    • (2000) Adv. Comput. Math , vol.12 , Issue.4 , pp. 273-288
    • Barthelmann, V.1    Novak, E.2    Ritter, K.3
  • 4
    • 70349536844 scopus 로고    scopus 로고
    • Gramian-based model reduction for data-sparse systems
    • U. Baur and P. Benner. Gramian-based model reduction for data-sparse systems. SIAM J. Sci. Comput., 31(1):776-798, 2008.
    • (2008) SIAM J. Sci. Comput , vol.31 , Issue.1 , pp. 776-798
    • Baur, U.1    Benner, P.2
  • 5
    • 1842535089 scopus 로고    scopus 로고
    • Solving large-scale control problems
    • P. Benner. Solving large-scale control problems. IEEE Control Systems Magazine, 14(1):44-59, 2004.
    • (2004) IEEE Control Systems Magazine , vol.14 , Issue.1 , pp. 44-59
    • Benner, P.1
  • 8
    • 2542503566 scopus 로고    scopus 로고
    • A multiparameter moment-matching model-reduction approach for generating geometrically parameterized interconnect performance models
    • May
    • L. Daniel, O. Siong, L. Chay, K. Lee, and J.White. A multiparameter moment-matching model-reduction approach for generating geometrically parameterized interconnect performance models. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., 23(5):678-693, May 2004.
    • (2004) IEEE Trans. Comput.-Aided Design Integr. Circuits Syst , vol.23 , Issue.5 , pp. 678-693
    • Daniel, L.1    Siong, O.2    Chay, L.3    Lee, K.4    White, J.5
  • 10
    • 61449142732 scopus 로고    scopus 로고
    • Ordnungsreduktion linearer zeitinvarianter Finite-Elemente-Modelle mit multivariater polynomieller Parametrierung (Model Order Reduction of Linear Finite Element Models Parameterized by Polynomials in Several Variables). at
    • O. Farle, V. Hill, P. Ingelström, and R. Dyczij-Edlinger. Ordnungsreduktion linearer zeitinvarianter Finite-Elemente-Modelle mit multivariater polynomieller Parametrierung (Model Order Reduction of Linear Finite Element Models Parameterized by Polynomials in Several Variables). at - Automatisierungstechnik, 54(4):161-169, 2006.
    • (2006) Automatisierungstechnik , vol.54 , Issue.4 , pp. 161-169
    • Farle, O.1    Hill, V.2    Ingelström, P.3    Dyczij-Edlinger, R.4
  • 11
    • 17444401366 scopus 로고    scopus 로고
    • Parameter independent model order reduction
    • L. Feng. Parameter independent model order reduction. Math. Comput. Simulation, 68(3):221-234, 2005.
    • (2005) Math. Comput. Simulation , vol.68 , Issue.3 , pp. 221-234
    • Feng, L.1
  • 12
    • 70349517829 scopus 로고    scopus 로고
    • L. Feng and P. Benner. A robust algorithm for parametric model order reduction based on implicit moment matching. PAMM Proc. Appl. Math. Mech., 7:1 021 501-1 021 502, 2008.
    • L. Feng and P. Benner. A robust algorithm for parametric model order reduction based on implicit moment matching. PAMM Proc. Appl. Math. Mech., 7:1 021 501-1 021 502, 2008.
  • 16
    • 39549092444 scopus 로고    scopus 로고
    • Smith-type methods for balanced truncation of large systems
    • P. Benner, V. Mehrmann, and D. Sorensen, editors, Dimension Reduction of Large-Scale Systems, of, Springer-Verlag, Berlin, Heidelberg, Germany
    • S. Gugercin and J.-R. Li. Smith-type methods for balanced truncation of large systems. In P. Benner, V. Mehrmann, and D. Sorensen, editors, Dimension Reduction of Large-Scale Systems, volume 45 of Lecture Notes in Computational Science and Engineering, pages 49-82. Springer-Verlag, Berlin, Heidelberg, Germany, 2005.
    • (2005) Lecture Notes in Computational Science and Engineering , vol.45 , pp. 49-82
    • Gugercin, S.1    Li, J.-R.2
  • 17
    • 0037276767 scopus 로고    scopus 로고
    • A modified low-rank Smith method for large-scale Lyapunov equations
    • S. Gugercin, D. C. Sorensen, and A. C. Antoulas. A modified low-rank Smith method for large-scale Lyapunov equations. Numer. Algorithms, 32(1):27-55, 2003.
    • (2003) Numer. Algorithms , vol.32 , Issue.1 , pp. 27-55
    • Gugercin, S.1    Sorensen, D.C.2    Antoulas, A.C.3
  • 19
    • 0028377922 scopus 로고
    • Krylov subspace methods for solving large Lyapunov equations
    • I. Jaimoukha and E. Kasenally. Krylov subspace methods for solving large Lyapunov equations. SIAM J. Numer. Anal., 31:227-251, 1994.
    • (1994) SIAM J. Numer. Anal , vol.31 , pp. 227-251
    • Jaimoukha, I.1    Kasenally, E.2
  • 21
    • 33745213726 scopus 로고    scopus 로고
    • Algorithm 847: Spinterp: Piecewise multilinear hierarchical sparse grid interpolation in MATLAB
    • A. Klimke and B. Wohlmuth. Algorithm 847: spinterp: Piecewise multilinear hierarchical sparse grid interpolation in MATLAB. ACM Transactions on Mathematical Software, 31(4), 2005.
    • (2005) ACM Transactions on Mathematical Software , vol.31 , Issue.4
    • Klimke, A.1    Wohlmuth, B.2
  • 22
    • 0037287244 scopus 로고    scopus 로고
    • Low rank solution of Lyapunov equations
    • J.-R. Li and J. White. Low rank solution of Lyapunov equations. SIAM J. Matrix Anal. Appl., 24(1):260-280, 2002.
    • (2002) SIAM J. Matrix Anal. Appl , vol.24 , Issue.1 , pp. 260-280
    • Li, J.-R.1    White, J.2
  • 23
    • 0019533482 scopus 로고
    • Principal component analysis in linear systems: Controllability, observability, and model reduction
    • B. C. Moore. Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans. Automat. Control, AC-26(1):17-32, 1981.
    • (1981) IEEE Trans. Automat. Control , vol.AC-26 , Issue.1 , pp. 17-32
    • Moore, B.C.1
  • 24
    • 70349547838 scopus 로고    scopus 로고
    • Convective thermal flow problems
    • P. Benner, V. Mehrmann, and D. Sorensen, editors, Dimension Reduction of Large-Scale Systems, of, Springer-Verlag, Berlin, Heidelberg, Germany
    • C. Moosmann and A. Greiner. Convective thermal flow problems. In P. Benner, V. Mehrmann, and D. Sorensen, editors, Dimension Reduction of Large-Scale Systems, volume 45 of Lecture Notes in Computational Science and Engineering, pages 341-343. Springer-Verlag, Berlin, Heidelberg, Germany, 2005.
    • (2005) Lecture Notes in Computational Science and Engineering , vol.45 , pp. 341-343
    • Moosmann, C.1    Greiner, A.2
  • 26
    • 0033295674 scopus 로고    scopus 로고
    • T. Penzl. A cyclic low-rank Smith method for large sparse Lyapunov equations. SIAM J. Sci. Comput., 21(4):1401-1418, 1999/00.
    • T. Penzl. A cyclic low-rank Smith method for large sparse Lyapunov equations. SIAM J. Sci. Comput., 21(4):1401-1418, 1999/00.
  • 27
    • 0000175612 scopus 로고
    • Numerical solution of large Lyapunov equations
    • M. A. Kaashoek, J.H. van Schuppen, and A. C.M. Ran, editors, Birkhäuser
    • Y. Saad. Numerical solution of large Lyapunov equations. In M. A. Kaashoek, J.H. van Schuppen, and A. C.M. Ran, editors, Signal Processing, Scattering, Operator Theory and Numerical Methods, pages 503-511. Birkhäuser, 1990.
    • (1990) Signal Processing, Scattering, Operator Theory and Numerical Methods , pp. 503-511
    • Saad, Y.1
  • 28
    • 44649084929 scopus 로고    scopus 로고
    • A new iterative method for solving large-scale Lyapunov matrix equations
    • V. Simoncini. A new iterative method for solving large-scale Lyapunov matrix equations. SIAM J. Sci. Comput., 29(3):1268-1288, 2007.
    • (2007) SIAM J. Sci. Comput , vol.29 , Issue.3 , pp. 1268-1288
    • Simoncini, V.1
  • 29
    • 0023439931 scopus 로고
    • Truncated balanced realization of a stable nonminimal state-space system
    • M. S. Tombs and I. Postlethwaite. Truncated balanced realization of a stable nonminimal state-space system. Internat. J. Control, 46(4):1319-1330, 1987.
    • (1987) Internat. J. Control , vol.46 , Issue.4 , pp. 1319-1330
    • Tombs, M.S.1    Postlethwaite, I.2
  • 30
    • 0001920020 scopus 로고    scopus 로고
    • A method for generating rational interpolant reduced order models of two-parameter linear systems
    • D. S. Weile, E. Michielssen, E. Grimme, and K. Gallivan. A method for generating rational interpolant reduced order models of two-parameter linear systems. Appl. Math. Lett., 12(5):93-102, 1999.
    • (1999) Appl. Math. Lett , vol.12 , Issue.5 , pp. 93-102
    • Weile, D.S.1    Michielssen, E.2    Grimme, E.3    Gallivan, K.4
  • 31
    • 34250126304 scopus 로고
    • On the multilevel splitting of finite element spaces
    • H. Yserentant. On the multilevel splitting of finite element spaces. Numer. Math., 49(4):379-412, 1986.
    • (1986) Numer. Math , vol.49 , Issue.4 , pp. 379-412
    • Yserentant, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.