Pade´ techniques for model reduction in linear system theory: a survey
Journal of Computational and Applied Mathematics
Journal of Approximation Theory
Reduction to tridiagonal form and minimal realizations
SIAM Journal on Matrix Analysis and Applications
A review on the inverse of symmetric tridiagonal and block tridiagonal matrices
SIAM Journal on Matrix Analysis and Applications
An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices
SIAM Journal on Scientific Computing
Balancing for nonlinear systems
Systems & Control Letters
An implementation of the QMR method based on coupled two-term recurrences
SIAM Journal on Scientific Computing
Oblique Projection Methods for Large Scale Model Reduction
SIAM Journal on Matrix Analysis and Applications
Algorithm 640: Efficient calculation of frequency response matrices from state space models
ACM Transactions on Mathematical Software (TOMS) - The MIT Press scientific computation series
Reduced-order modeling of large linear subcircuits via a block Lanczos algorithm
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
QMRPACK: a package of QMR algorithms
ACM Transactions on Mathematical Software (TOMS)
Implicitly Restarted Krylov Subspace Methods for Stable Partial Realizations
SIAM Journal on Matrix Analysis and Applications
PRIMA: passive reduced-order interconnect macromodeling algorithm
ICCAD '97 Proceedings of the 1997 IEEE/ACM international conference on Computer-aided design
Projection frameworks for model reduction of weakly nonlinear systems
Proceedings of the 37th Annual Design Automation Conference
Practical considerations for passive reduction of RLC circuits
ICCAD '99 Proceedings of the 1999 IEEE/ACM international conference on Computer-aided design
A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
SIAM Journal on Scientific Computing
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Krylov-subspace methods for reduced-order modeling in circuit simulation
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Microsystem design
Asymptotic Waveform Evaluation and Moment Matching for Interconnect Analysis
Asymptotic Waveform Evaluation and Moment Matching for Interconnect Analysis
Computer Methods for Circuit Analysis and Design
Computer Methods for Circuit Analysis and Design
A Symmetric Band Lanczos Process Based on Coupled Recurrences and Some Applications
SIAM Journal on Scientific Computing
Accuracy of Two Three-term and Three Two-term Recurrences for Krylov Space Solvers
SIAM Journal on Matrix Analysis and Applications
The Quadratic Eigenvalue Problem
SIAM Review
Simulating the Behavior of MEMS Devices: Computational Methods and Needs
IEEE Computational Science & Engineering
Error bound for reduced system model by Pade approximation via the Lanczos process
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Emerging simulation approaches for micromachined devices
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Efficient linear circuit analysis by Pade approximation via the Lanczos process
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Piecewise polynomial nonlinear model reduction
Proceedings of the 40th annual Design Automation Conference
Parametric reduced order modeling for interconnect analysis
Proceedings of the 2004 Asia and South Pacific Design Automation Conference
A priori hyperreduction method: an adaptive approach
Journal of Computational Physics
A general framework for automated physics-based reduced-order modeling of electromechanical systems
Proceedings of the 2007 Summer Computer Simulation Conference
A parallel method for large sparse generalized eigenvalue problems using a GridRPC system
Future Generation Computer Systems
International Journal of Computer Mathematics
A two-directional Arnoldi process and its application to parametric model order reduction
Journal of Computational and Applied Mathematics
Order reduction of bilinear MIMO dynamical systems using new block Krylov subspaces
Computers & Mathematics with Applications
QLMOR: a new projection-based approach for nonlinear model order reduction
Proceedings of the 2009 International Conference on Computer-Aided Design
A master-worker type eigensolver for molecular orbital computations
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Coupled electrothermal-mechanical analysis for MEMS via model order reduction
Finite Elements in Analysis and Design
Nonlinear Model Reduction via Discrete Empirical Interpolation
SIAM Journal on Scientific Computing
A Krylov enhanced proper orthogonal decomposition method for efficient nonlinear model reduction
Finite Elements in Analysis and Design
Structural and Multidisciplinary Optimization
Model order reduction via eigen decomposition analysis
International Journal of Computer Applications in Technology
On Efficient Numerical Approximation of the Bilinear Form $c^*A^{-1}b$
SIAM Journal on Scientific Computing
Structure-preserving model reduction
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
A parallel method for large sparse generalized eigenvalue problems by OmniRPC in a grid environment
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Model order reduction for dynamic simulation of beams with forcing and geometric nonlinearities
Finite Elements in Analysis and Design
Journal of Electronic Testing: Theory and Applications
Mathematics and Computers in Simulation
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In recent years, a great deal of attention has been devoted to Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. The surge of interest was triggered by the pressing need for efficient numerical techniques for simulations of extremely large-scale dynamical systems arising from circuit simulation, structural dynamics, and microelectromechanical systems. In this paper, we begin with a tutorial of a Lanczos process based Krylov subspace technique for reduced-order modeling of linear dynamical systems, and then give an overview of the recent progress in other Krylov subspace techniques for a variety of dynamical systems, including second-order and nonlinear systems. Case studies arising from circuit simulation, structural dynamics and microelectromechanical systems are presented.