Laguerre-Gram reduced-order modeling

Amghayrir, A.; Tanguy, Noël; Brehonnet, P.; Vilbe, P.; Calvez, L.C.

doi:10.1109/tac.2005.854653

Cited by 19 publications

(14 citation statements)

References 17 publications

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“…Note that for the special case of single parameter Laguerre functions, i.e. a l ¼ a 2 R, the stability of GðsÞ was already proven in [19].…”

Section: Stabilitymentioning

confidence: 94%

“…Note that relation (17) is a generalization of the technique already presented by some of the authors in [19] in a context of model order reduction of 'single parameter' Laguerre expansions. The same relation (17) is also exploited in [20] to derive rational models using a different approach.…”

Section: Computational Aspectmentioning

confidence: 99%

“…With the algorithm described in the present paper, both the issue of parameter selection and the issue of subsequently deriving a low order model are solved. The considered system is a distributed RC-circuit whose irrational transfer function is [27,19] ; with RC ¼ 1:…”

Section: Numerical Examplesmentioning

confidence: 99%

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Parameter optimization of orthonormal basis functions for efficient rational approximations

Tanguy

Iassamen

Telescu

et al. 2015

Applied Mathematical Modelling

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International audienceIn this paper, the authors present an efficient procedure for optimal placement of poles in rational approximations by Müntz-Laguerre functions. The technique is formulated as the minimization of a quadratic criterion and the linear equations involved are efficiently expressed using the orthonormal basis functions. The presented technique has direct application in rational approximation and model order reduction of large-degree or infinite-dimensional systems. An efficient choice of parameters in orthogonal Müntz-Laguerre approximation Model order reduction of large-degree or infinite-dimensional systems The choice of Müntz-Laguerre parameters is based on a least squares optimization Abstract: In this paper, the authors present an efficient procedure for optimal placement of poles in rational approximations by Müntz-Laguerre functions. The technique is formulated as the minimization of a quadratic criterion and the linear equations involved are efficiently expressed using the orthonormal basis functions. The presented technique has direct application in rational approximation and model order reduction of large-degree or infinite-dimensional systems

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“…Note that for the special case of single parameter Laguerre functions, i.e. a l ¼ a 2 R, the stability of GðsÞ was already proven in [19].…”

Section: Stabilitymentioning

confidence: 94%

Section: Computational Aspectmentioning

confidence: 99%

See 1 more Smart Citation

Parameter optimization of orthonormal basis functions for efficient rational approximations

Tanguy

Iassamen

Telescu

et al. 2015

Applied Mathematical Modelling

Self Cite

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“…In previous papers [1,5,6] we presented a Laguerre-Gram reduction method and its applications to VLSI circuits. The Laguerre-Gram method is basically a two step algorithm.…”

Section: Introductionmentioning

confidence: 99%

Stable model order reduction method using Kautz functions: Application to VLSI circuits

Telescu

Brehonnet

Tanguy

et al. 2007

2007 IEEE Workshop on Signal Propagation on Interconnects

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To cite this version:Mihai Telescu, Pascale Bréhonnet, Noël Tanguy, Pierre Vilbé. AbstractIn previous papers we presented MOR (Model Order Reduction) methods based on the construction of a Gram matrix subsequent to a decomposition in Laguerre series. In this paper we propose an alternative solution using Kautz series, more adequate for modeling poorly damped systems. IntroductionEfficient reduced order modeling techniques have become a valuable tool for system designers in recent years, particularly in the field of VLSI circuit interconnects. In previous papers [1,5,6] we presented a Laguerre-Gram reduction method and its applications to VLSI circuits. The Laguerre-Gram method is basically a two step algorithm. The first step supposes a decomposition of the original transfer function (or transfer functions in the MIMO case) in a Laguerre series. With the Laguerre spectrum (or spectra) made available an approximation basis is constructed by repeated application of an adequate operator and a stable rational model is readily calculated. Some difficulties may however appear if the original system displays a slowly attenuated oscillating behavior. The method described in this paper proves a viable alternative in such cases. It follows the same two-step scenario describe above but it is no longer based on single-pole Laguerre functions but on two-pole Kautz functions more appropriate for modeling resonant systems.

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“…Tools have therefore been developed to enable the approximation of full interconnect models by simpler, more versatile ones. The method we propose in this paper benefits from recent research on Laguerre representations [2], [6].…”

Section: Introductionmentioning

confidence: 99%