An introduction to infinite-dimensional linear systems theory
An introduction to infinite-dimensional linear systems theory
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
Stability and Stabilization of Time-Delay Systems (Advances in Design & Control) (Advances in Design and Control)
Convergence of the Dominant Pole Algorithm and Rayleigh Quotient Iteration
SIAM Journal on Matrix Analysis and Applications
Computing Transfer Function Dominant Poles of Large-Scale Second-Order Dynamical Systems
SIAM Journal on Scientific Computing
A Krylov Method for the Delay Eigenvalue Problem
SIAM Journal on Scientific Computing
PRIMA: passive reduced-order interconnect macromodeling algorithm
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Parametric dominant pole algorithm for parametric model order reduction
Journal of Computational and Applied Mathematics
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The method known as the dominant pole algorithm (DPA) has previously been successfully used in combination with model order reduction techniques to approximate standard linear time-invariant dynamical systems and second order dynamical systems. In this paper, we show how this approach can be adapted to a class of second order delay systems, which are large scale nonlinear problems whose transfer functions have an infinite number of simple poles. Deflation is a very important ingredient for this type of methods. Because of the nonlinearity, many deflation approaches for linear systems are not applicable. We therefore propose an alternative technique that essentially removes computed poles from the system@?s input and output vectors. In general, this technique changes the residues, and hence, modifies the order of dominance of the poles, but we prove that, under certain conditions, the residues stay near the original residues. The new algorithm is illustrated by numerical examples.