Global harmony: coupled noise analysis for full-chip RC interconnect networks
ICCAD '97 Proceedings of the 1997 IEEE/ACM international conference on Computer-aided design
Microelectronic Engineering
Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems
Applied Numerical Mathematics
Poor Man's TBR: A Simple Model Reduction Scheme
Proceedings of the conference on Design, automation and test in Europe - Volume 2
Exploiting input information in a model reduction algorithm for massively coupled parasitic networks
Proceedings of the 41st annual Design Automation Conference
Use of near-breakdowns in the block Arnoldi method for solving large Sylvester equations
Applied Numerical Mathematics
Efficient simulation of nonuniform transmission lines using integrated congruence transform
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation
SIAM Journal on Numerical Analysis
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The aim of this paper is to consider approximating a linear transfer function $F(s)$ of McMillan degree $N$, by one of McMillan degree $m$ in which $N\gg m$ and where $N$ is large. Krylov subspace methods are employed to construct bases to parts of the controllability and observability subspaces associated with the state space realisation of $F(s)$. Low rank approximate grammians are computed via the solutions to low dimensional Lyapunov equations and computable expressions for the approximation errors incurred are derived. We show that the low rank approximate grammians are the exact grammians to a perturbed linear system in which the perturbation is restricted to the transition matrix, and furthermore, this perturbation has at most ${\rm rank}=2$. This paper demonstrates that this perturbed linear system is equivalent to a low dimensional linear system with state dimension no greater than $m$. Finally, exact low dimensional expressions for the ${\cal L}^{\infty}$ norm of the errors are derived. The model reduction of discrete time linear systems is considered via the use of the same Krylov schemes. Finally, the behaviour of these algorithms is illustrated on two large scale examples.