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Volumn 43, Issue 4, 2005, Pages 1693-1714

Error estimation for reduced-order models of dynamical systems

Author keywords

Adjoint method; Model reduction; Proper orthogonal decomposition; Small sample statistical condition estimation

Indexed keywords

ADJOINT METHOD; MODEL REDUCTION; PROPER ORTHOGONAL DECOMPOSITION; SMALL SAMPLE STATISTICAL CONDITION ESTIMATION;

EID: 33747163532     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/040603541     Document Type: Article
Times cited : (57)

References (33)
  • 1
    • 0033372615 scopus 로고    scopus 로고
    • A two-layer model with empirical linear corrections and reduced order for studies of internal climate variability
    • U. ACHATZ AND G. BRANSTATOR, A two-layer model with empirical linear corrections and reduced order for studies of internal climate variability, J. Atmospheric Sci., 56 (1999), pp. 3140-3160.
    • (1999) J. Atmospheric Sci. , vol.56 , pp. 3140-3160
    • Achatz, U.1    Branstator, G.2
  • 2
    • 0005387477 scopus 로고    scopus 로고
    • Approximation of large-scale dynamical systems: An overview
    • Rice University, Houston, TX
    • A.C. ANTOULAS AND D.C. SORENSEN, Approximation of Large-Scale Dynamical Systems: An Overview, Tech. report TR0101, Rice University, Houston, TX, 2001.
    • (2001) Tech. Report , vol.TR0101
    • Antoulas, A.C.1    Sorensen, D.C.2
  • 3
    • 0036568121 scopus 로고    scopus 로고
    • A novel, efficient and reliable method for thermal process design and optimization
    • E. BALSA-CANTO, A.A. ALONSO, AND J.R. BANGA, A novel, efficient and reliable method for thermal process design and optimization, J. Food Engrg., 52 (2002), pp. 227-247.
    • (2002) J. Food Engrg. , vol.52 , pp. 227-247
    • Balsa-Canto, E.1    Alonso, A.A.2    Banga, J.R.3
  • 4
    • 16244403904 scopus 로고    scopus 로고
    • A posteriori error estimation and global error control for ordinary differential equations by the adjoint method
    • Y. CAO AND L.R. PETZOLD, A posteriori error estimation and global error control for ordinary differential equations by the adjoint method, SIAM J. Sci. Comput., 26 (2004), pp. 359-374.
    • (2004) SIAM J. Sci. Comput. , vol.26 , pp. 359-374
    • Cao, Y.1    Petzold, L.R.2
  • 5
    • 0037603391 scopus 로고    scopus 로고
    • Application of proper orthogonal decomposition to a supersonic axisymmetric jet
    • E. CARABALLO, M. SAMINY, J. SCOTT, S. NARAYAN, AND J. DEBONIS, Application of proper orthogonal decomposition to a supersonic axisymmetric jet, AIAA J., 41 (2003), pp. 866-877.
    • (2003) AIAA J. , vol.41 , pp. 866-877
    • Caraballo, E.1    Saminy, M.2    Scott, J.3    Narayan, S.4    Debonis, J.5
  • 6
    • 0037359707 scopus 로고    scopus 로고
    • Proper orthogonal decomposition of turbine rotor-stator interaction
    • P.G.A. CIZMAS AND A. PALACIOS, Proper orthogonal decomposition of turbine rotor-stator interaction, J. Propul. Power, 19 (2003), pp. 268-281.
    • (2003) J. Propul. Power , vol.19 , pp. 268-281
    • Cizmas, P.G.A.1    Palacios, A.2
  • 7
    • 4844222391 scopus 로고    scopus 로고
    • Strategies for model reduction: Comparing different optimal bases
    • D.T. CROMMELIN AND A.J. MAJDA, Strategies for model reduction: Comparing different optimal bases, J. Atmospheric Sci., 61 (2004), pp. 2206-2217.
    • (2004) J. Atmospheric Sci. , vol.61 , pp. 2206-2217
    • Crommelin, D.T.1    Majda, A.J.2
  • 8
    • 0035301795 scopus 로고    scopus 로고
    • Extratropical low-frequency variability as a low-dimensional problem I: A simplified model
    • F. D'ANDREA AND R. VAUTARD, Extratropical low-frequency variability as a low-dimensional problem I: A simplified model, Q.J.R. Meterol. Soc., 127 (2001), pp. 1357-1375.
    • (2001) Q.J.R. Meterol. Soc. , vol.127 , pp. 1357-1375
    • D'Andrea, F.1    Vautard, R.2
  • 10
  • 13
    • 33747173093 scopus 로고    scopus 로고
    • Error Estimation for Reduced Order Models of Dynamical Systems
    • Lawrence Livermore National Laboratory, Livermore, CA
    • C. HOMESCU, L.R. PETZOLD, AND R. SERBAN, Error Estimation for Reduced Order Models of Dynamical Systems, Tech. report UCRL-TR-201494, Lawrence Livermore National Laboratory, Livermore, CA, 2003.
    • (2003) Tech. Report , vol.UCRL-TR-201494
    • Homescu, C.1    Petzold, L.R.2    Serban, R.3
  • 15
    • 0002565781 scopus 로고
    • Small-sample statistical condition estimates for general matrix functions
    • C.S. KENNEY AND A.J. LAUB, Small-sample statistical condition estimates for general matrix functions, SIAM J. Sci. Comput., 15 (1994), pp. 36-61.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 36-61
    • Kenney, C.S.1    Laub, A.J.2
  • 16
    • 0031177968 scopus 로고    scopus 로고
    • Dynamic wind pressures acting on a tall building model - Proper orthogonal decomposition
    • H. KIKUCHI, Y. TAMURA, H. UEDA, AND K. HIBI, Dynamic wind pressures acting on a tall building model - proper orthogonal decomposition, J. Wind. Eng. Ind. Aerod., 71 (1997), pp. 631-646.
    • (1997) J. Wind. Eng. Ind. Aerod. , vol.71 , pp. 631-646
    • Kikuchi, H.1    Tamura, Y.2    Ueda, H.3    Hibi, K.4
  • 17
    • 0242300785 scopus 로고    scopus 로고
    • Model-order reduction of nonlinear models of electromagnetic phased-array hyperthermia
    • M.E. KOWALSKI AND H.M. JIN, Model-order reduction of nonlinear models of electromagnetic phased-array hyperthermia, IEEE T. Bio-Med. Eng., 50 (2003), pp. 1243-1254.
    • (2003) IEEE T. Bio-med. Eng. , vol.50 , pp. 1243-1254
    • Kowalski, M.E.1    Jin, H.M.2
  • 18
    • 0033177060 scopus 로고    scopus 로고
    • Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition
    • K. KUNISCH AND S. VOLKWEIN, Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition, J. Optim. Theory Appl., 102 (1999), pp. 345-371.
    • (1999) J. Optim. Theory Appl. , vol.102 , pp. 345-371
    • Kunisch, K.1    Volkwein, S.2
  • 19
    • 0038693394 scopus 로고    scopus 로고
    • Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics
    • K. KUNISCH AND S. VOLKWEIN, Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics, SIAM J. Numer. Anal., 40 (2002), pp. 492-515.
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 492-515
    • Kunisch, K.1    Volkwein, S.2
  • 20
    • 23544480853 scopus 로고    scopus 로고
    • Dynamic domain decomposition and error correction for reduced order models
    • 41st AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV
    • P.A. LEGRESLEY AND J.J. ALONSO, Dynamic Domain Decomposition and Error Correction for Reduced Order Models, AIAA Paper 2003-0250, 41st AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV, 2003.
    • (2003) AIAA Paper , vol.2003 , Issue.250
    • Legresley, P.A.1    Alonso, J.J.2
  • 21
    • 0141483642 scopus 로고    scopus 로고
    • Low-dimensional dynamical system model for observed coherent structures in ocean satellite data
    • C. LOPEZ AND E. GARCIA-HERNÁNDEZ, Low-dimensional dynamical system model for observed coherent structures in ocean satellite data, Phys. A, 328 (2003), pp. 233-250.
    • (2003) Phys. A , vol.328 , pp. 233-250
    • Lopez, C.1    Garcia-Hernández, E.2
  • 22
    • 34250013894 scopus 로고    scopus 로고
    • Reduced order modeling for a one-dimensional nozzle flow with moving shocks
    • AIAA 15th Computational Fluid Dynamics Conference, Anaheim, CA
    • D.J. LUCIA, P.I. KING, M.E. OXLEY, AND P.S. BERAN, Reduced Order Modeling for a One-Dimensional Nozzle Flow with Moving Shocks, AIAA Paper 01-2602, AIAA 15th Computational Fluid Dynamics Conference, Anaheim, CA, 2001.
    • (2001) AIAA Paper , vol.1 , Issue.2602
    • Lucia, D.J.1    King, P.I.2    Oxley, M.E.3    Beran, P.S.4
  • 23
    • 0037053486 scopus 로고    scopus 로고
    • A low-dimensional model for simulating three-dimensional cylinder flow
    • X. MA AND G.E. KARNIADAKIS, A low-dimensional model for simulating three-dimensional cylinder flow, J. Fluid Mech., 458 (2002), pp. 181-190.
    • (2002) J. Fluid Mech. , vol.458 , pp. 181-190
    • Ma, X.1    Karniadakis, G.E.2
  • 24
    • 0043127074 scopus 로고    scopus 로고
    • Systematic strategies for stochastic mode reduction in climate
    • A.J. MAJDA, I. TIMOKEYEV, AND E. VANDEN-EIJNDEN, Systematic strategies for stochastic mode reduction in climate, J. Atmospheric Sci., 60 (2003), pp. 1705-1722.
    • (2003) J. Atmospheric Sci. , vol.60 , pp. 1705-1722
    • Majda, A.J.1    Timokeyev, I.2    Vanden-Eijnden, E.3
  • 25
    • 0037481177 scopus 로고    scopus 로고
    • Efficient model reduction in non-linear dynamics using the Karhunen-Loeve expansion and dual-weighted-residual methods
    • M. MEYER AND H.G. MATTHIES, Efficient model reduction in non-linear dynamics using the Karhunen-Loeve expansion and dual-weighted-residual methods, Comput. Mech., 31 (2003), pp. 179-191.
    • (2003) Comput. Mech. , vol.31 , pp. 179-191
    • Meyer, M.1    Matthies, H.G.2
  • 26
    • 9244228981 scopus 로고    scopus 로고
    • A new look at proper orthogonal decomposition
    • M. RATHINAM AND L.R. PETZOLD, A new look at proper orthogonal decomposition, SIAM J. Numer. Anal., 41 (2003), pp. 1893-1925.
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 1893-1925
    • Rathinam, M.1    Petzold, L.R.2
  • 27
    • 0034327551 scopus 로고    scopus 로고
    • A reduced-order approach for optimal control of fluids using proper orthogonal decomposition
    • S.S. RAVINDRAN, A reduced-order approach for optimal control of fluids using proper orthogonal decomposition, Internat. J. Numer. Methods Fluids, 34 (2000), pp. 425 448.
    • (2000) Internat. J. Numer. Methods Fluids , vol.34 , pp. 425448
    • Ravindran, S.S.1
  • 28
    • 0035440960 scopus 로고    scopus 로고
    • Design of an aeroelastic delta wing model for active flutter control
    • J.A. RULE, R.E. RICHARD. AND R.L. CLARK, Design of an aeroelastic delta wing model for active flutter control, J. Guid. Control Dynam., 24 (2001), pp. 918-924.
    • (2001) J. Guid. Control Dynam. , vol.24 , pp. 918-924
    • Rule, J.A.1    Richard, R.E.2    Clark, R.L.3
  • 29
    • 0031200721 scopus 로고    scopus 로고
    • Baroclinic empirical orthogonal functions as basis functions in an atmospheric model
    • F.M. SELTEN, Baroclinic empirical orthogonal functions as basis functions in an atmospheric model, J. Atmospheric Sci., 54 (1997), pp. 2100-2114.
    • (1997) J. Atmospheric Sci. , vol.54 , pp. 2100-2114
    • Selten, F.M.1
  • 30
    • 0038819101 scopus 로고    scopus 로고
    • Creating compact models of complex electronic systems: An overview and suggested use of existing model reduction and experimental system identification tools
    • B. SHAPIRO, Creating compact models of complex electronic systems: An overview and suggested use of existing model reduction and experimental system identification tools, IEEE T. Comp. Pack. T., 26 (2003), pp. 165-172.
    • (2003) IEEE T. Comp. Pack. T. , vol.26 , pp. 165-172
    • Shapiro, B.1
  • 31
    • 0036609576 scopus 로고    scopus 로고
    • Power distribution analysis of VLSI interconnects using model order reduction
    • Y. SHIN AND T. SAKURAI, Power distribution analysis of VLSI interconnects using model order reduction, IEEE T. Comput. Aid. D., 21 (2002), pp. 739-745.
    • (2002) IEEE T. Comput. Aid. D. , vol.21 , pp. 739-745
    • Shin, Y.1    Sakurai, T.2
  • 33
    • 0001637748 scopus 로고
    • Gauss-Seidel iteration for stiff ODEs from chemical kinetics
    • J.G. VERWER, Gauss-Seidel iteration for stiff ODEs from chemical kinetics, SIAM J. Sci. Comput., 15 (1994), pp. 1243-1250.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 1243-1250
    • Verwer, J.G.1


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