Algorithms for model reduction of large dynamical systems

[1]  H. H. Rachford,et al.  The Numerical Solution of Parabolic and Elliptic Differential Equations , 1955 .

[2]  Louis Weinberg,et al.  Network Analysis and Synthesis , 1962 .

[3]  E. Davison,et al.  On "A method for simplifying linear dynamic systems" , 1966 .

[4]  R. A. Smith.  Matrix Equation $XA + BX = C$ , 1968 .

[5]  H. Schwarz.  Tridiagonalization of a symetric band matrix , 1968 .

[6]  P. Lancaster.  Explicit Solutions of Linear Matrix Equations , 1970 .

[7]  R. Willoughby.  Sparse matrices and their applications , 1972 .

[8]  Elizabeth Cuthill,et al.  Several Strategies for Reducing the Bandwidth of Matrices , 1972 .

[9]  Richard H. Bartels,et al.  Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4] , 1972, Commun. ACM.

[10]  W. Gragg.  Matrix interpretations and applications of the continued fraction algorithm , 1974 .

[11]  Y. Shamash.  Model reduction using the Routh stability criterion and the Padé approximation technique , 1975 .

[12]  R. Roberts,et al.  Roundoff noise in digital filters: Frequency transformations and invariants , 1976 .

[13]  J. D. Roberts,et al.  Linear model reduction and solution of the algebraic Riccati equation by use of the sign function , 1980 .

[14]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[15]  S. Hammarling.  Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation , 1982 .

[16]  K. Fernando,et al.  Singular perturbational model reduction of balanced systems , 1982 .

[17]  Gene H. Golub,et al.  Matrix computations , 1983 .

[18]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[19]  D. Enns.  Model reduction with balanced realizations: An error bound and a frequency weighted generalization , 1984, The 23rd IEEE Conference on Decision and Control.

[20]  I. Postlethwaite,et al.  Truncated balanced realization of a stable non-minimal state-space system , 1987 .

[21]  E. Wachspress.  Iterative solution of the Lyapunov matrix equation , 1988 .

[22]  Y. Saad,et al.  Numerical solution of large Lyapunov equations , 1989 .

[23]  M. Safonov,et al.  A Schur method for balanced-truncation model reduction , 1989 .

[24]  George A. Geist.  Reduction of a general matrix to tridiagonal form using a hypercube multiprocessor , 1991 .

[25]  Lawrence T. Pileggi,et al.  Asymptotic waveform evaluation for timing analysis , 1990, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[26]  M. A. Kaashoek,et al.  Signal processing, scattering and operator theory, and numerical methods , 1990 .

[27]  A. Laub,et al.  Parallel algorithms for algebraic Riccati equations , 1991 .

[28]  L. Reichel,et al.  Krylov-subspace methods for the Sylvester equation , 1992 .

[29]  P. Dooren,et al.  Asymptotic Waveform Evaluation via a Lanczos Method , 1994 .

[30]  A. Laub,et al.  Approximate solution of large sparse Lyapunov equations , 1994, IEEE Trans. Autom. Control..

[31]  I. Jaimoukha,et al.  Krylov subspace methods for solving large Lyapunov equations , 1994 .

[32]  Roland W. Freund,et al.  Efficient linear circuit analysis by Pade´ approximation via the Lanczos process , 1994, EURO-DAC '94.

[33]  Imad M. Jaimoukha,et al.  Oblique Production Methods for Large Scale Model Reduction , 1995, SIAM J. Matrix Anal. Appl..

[34]  Leiba Rodman,et al.  Algebraic Riccati equations , 1995 .

[35]  K. Poolla,et al.  NUMERICAL SOLUTION OF THE LYAPUNOV EQUATION BY APPROXIMATE POWER ITERATION , 1996 .

[36]  I. Jaimoukha,et al.  Implicitly Restarted Krylov Subspace Methods for Stable Partial Realizations , 1997, SIAM J. Matrix Anal. Appl..

[37]  I. Jaimoukha.  A general minimal residual Krylov subspace method for large-scale model reduction , 1997, IEEE Trans. Autom. Control..

[38]  Ernst Dieter Gilles,et al.  Automatic control of the simulated moving bed process for C8 aromatics separation using asymptotically exact input/output-linearization , 1999 .

[39]  Biswa Nath Datta,et al.  Applied and computational control, signals, and circuits , 1999 .

[40]  Enrique S. Quintana-Ortí,et al.  Parallel Distributed Solvers for Large Stable Generalized Lyapunov Equations , 1999, Parallel Process. Lett..

[41]  Marko Huhtanen.  Iterative Model Reduction of Large State-Space Systems , 1999 .

[42]  Thilo Penzl,et al.  A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations , 1998, SIAM J. Sci. Comput..

[43]  R. Freund.  Reduced-Order Modeling Techniques Based on Krylov Subspaces and Their Use in Circuit Simulation , 1999 .

[44]  Enrique S. Quintana-Ortí,et al.  Balanced Truncation Model Reduction of Large-Scale Dense Systems on Parallel Computers , 2000 .

[45]  Thilo Penzl.  Eigenvalue decay bounds for solutions of Lyapunov equations: the symmetric case , 2000 .

[46]  F. Tröltzsch,et al.  Fast solution of optimal control problems in the selective cooling of steel , 2001 .

[47]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[48]  Paul Van Dooren,et al.  A rational Lanczos algorithm for model reduction , 1996, Numerical Algorithms.