Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems

Applied Numerical Mathematics

Volumn 43, Issue 1-2, 2002, Pages 9-44

  Bai, Zhaojun ^a  

^a University of California   (United States)

Author keywords

Dynamical systems; Krylov subspace technique; Moment matching; Pad approximation; Passivity; Reduced order modeling; Stability; Transfer function

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; LINEAR SYSTEMS; MICROELECTROMECHANICAL DEVICES; SYSTEM STABILITY; TRANSFER FUNCTIONS;

DYNAMICAL SYSTEMS;

LARGE SCALE SYSTEMS;

EID: 0036776433     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(02)00116-2     Document Type: Conference Paper

References (89)

1. An approach to macromodeling of MEMS for nonlinear dynamic simulation
2. New numerical techniques and tools in SUGAR for 3D MEMS simulation
3. Eigenvalue-based characterization and test for positive realness of scalar transfer functions
4. A partial Padé-via-Lanczos method for reduced-order modeling
5. A symmetric band Lanczos process based on coupled recurrence and some applications
6. Error bounds for reduced system model by Padé approximation via the Lanczos process
7. Error estimation of the Padé approximation of transfer functions via the Lanczos process
8. Krylov subspace methods on state-space control models
9. Partial Padé approximation
10. Synthesis of a finite two terminal network whose driving-point impedance is a prescribed function of frequency
11. Padé techniques for model reduction in linear system theory: A survey
12. An algorithm for automatic model-order reduction of nonlinear MEMS devices
13. A quadratic method for nonlinear model order reduction
14. MEMS simulation using SUGAR v0.5
15. Block-Krylov component synthesis method for structural model reduction
16. Model reductions using a projection formulation
17. Efficient linear circuit analysis by Padé approximation via the Lanczos process
18. Reduced-order modeling techniques based on Krylov subspaces and their use in circuit simulation
19. Band Lanczos method (Section 4.6)
20. Krylov-subspace methods for reduced-order modeling in circuit simulation
21. Small-signal circuit analysis and sensitivity computations with the PVL algorithm
22. Reduced-order modeling of large linear subcircuits via a block Lanczos algorithm
23. The SyMPVL algorithm and its applications to interconnect simulation
24. An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices
25. An implementation of the QMR method based on coupled two-term recurrences
26. QMRPACK: A package of QMR algorithms
27. Computer-aided generation of nonlinear reduced-order dynamic macromodels - I: Non-stress-stiffened case
28. Asymptotic waveform evaluation via a Lanczos method
29. Calculation of Gauss quadrature with multiple free and fixed knots
30. Matrix interpretations and applications of the continued fraction algorithm
31. On the partial realization problem
32. Model reduction of state space systems via an implicitly restarted Lanczos method
33. Accuracy of two three-term and three two-term recurrences for Krylov space solvers
34. Numerical solution of the stable, non-negative definite Lyapunov equation
35. Implicitly restarted Krylov subspace methods for stable partial realizations
36. Oblique projection methods for large scale model reduction
37. A subspace approach to balanced truncation for model reduction of nonlinear control systems
38. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
39. Efficient calculation of frequency response matrices from state space models
40. A review of the inverse of symmetric tridiagonal and block tridiagonal matrices
41. Principal component analysis in linear systems: Controllability, observability, and model reduction
42. Emerging simulation approaches for micromachined devices
43. Dynamics analysis of structures using Lanczos coordinators
44. Practical considerations for passive reduction of RLC circuits
45. PRIMA: Passive reduced-order interconnect macromodeling algorithm
46. Reduction to tridiagonal form and minimal realizations
47. Relatively robust representation of symmetric tridiagonal
48. Multiple solutions in electrostatic MEMS
49. A cyclic low-rank Smith method for large sparse Lyapunov equations
50. Automated extraction of nonlinear circuit macromodels
51. Projection frameworks for model reduction of weakly nonlinear systems
52. Asymptotic waveform evaluation for timing analysis
53. Automatic generation of small-signal dynamic macromodels from 3-D simulation
54. An iterative method for simulation of large scale modular systems using reduced order models
55. Equivalent circuit models for three-dimensional multiconductor systems
56. Implementation aspects of band Lanczos algorithms for computation of eigenvalues of large sparse symmetric matrices
57. Balancing for nonlinear systems
58. Simulating the behavior of MEMS devices: Computational methods and needs
59. Linear system with a quadratic parameter and application to structural dynamics
60. Model reduction and control of flexible structures using Krylov vectors
61. The quadratic eigenvalue problem
62. Gramian based model reduction of large-scale dynamical systems
63. An Arnoldi approach for generalization of reduced-order models for turbomachinery
64. A convergence analysis for nonsymmetric Lanczos algorithms