Sylvester equations and projection-based model reduction
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
SOAR: A Second-order Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem
SIAM Journal on Matrix Analysis and Applications
Dimension Reduction of Large-Scale Second-Order Dynamical Systems via a Second-Order Arnoldi Method
SIAM Journal on Scientific Computing
Error Estimations of Arnoldi-Based Interconnect Model-Order Reductions
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Proceedings of the 2005 Asia and South Pacific Design Automation Conference
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Advanced Model Order Reduction Techniques in VLSI Design
Advanced Model Order Reduction Techniques in VLSI Design
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Model-order reductions for MIMO systems using global Krylov subspace methods
Mathematics and Computers in Simulation
PRIMA: passive reduced-order interconnect macromodeling algorithm
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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This paper investigates structure preserving model-order reductions of the MIMO second-order system. By extending the previous SISO second-order Arnoldi (SOAR) algorithm, both block Arnoldi methods and global Arnoldi methods will be investigated. Analytic expressions of system moments and output moments will be derived analytically in terms of the upper Hessenberg matrix. By employing the so-called congruence transformation, the system data of the reduced second-order system will be obtained. Relationships among these coefficients will also be derived. Simulations about practical engineering applications will be performed to illustrate the feasibility and the efficiency of these two classes of model reductions.