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The Laguerre iteration in solving the symmetric tridiagonal eigenproblem, revisited
SIAM Journal on Scientific Computing
Robust rational function approximation algorithm for model generation
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
SIAM Journal on Scientific Computing
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Extended Hamiltonian pencil for passivity assessment and enforcement for S-parameter systems
Proceedings of the Conference on Design, Automation and Test in Europe
A novel framework for passive macro-modeling
Proceedings of the 48th Design Automation Conference
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Passivity is an important property for a macro-model generated from measured or simulated data. Existence of purely imaginary eigenvalues of a Hamiltonian matrix provides useful information in assessing and correcting the passivity of a system. Since direct computation of eigenvalues is very expensive for large-scale systems, several authors have proposed to solve iteratively for a subset of the eigenvalues based on heuristic sampling along the imaginary axis. However, completeness is not guaranteed in such methods and thus potential risk of missing important eigenvalues is difficult to avoid. In this paper we are aiming at finding all eigenvalues efficiently to avoid both the high cost and the potential risk of missing important eigenvalues. The idea of the proposed method is to convert the Hamiltonian matrix to an equivalent sparse form, termed the "extended Hamiltonian pencil", and solve for its eigenvalues efficiently using a special eigensolver. Experiments on several realistic systems demonstrate an 80X speed-up compared with standard direct eigensolvers.