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Parameter optimization of orthonormal basis functions for efficient rational approximations

Noël Tanguy 1, 2 Nadia Iassamen 1, 2 Mihai Telescu 1, 2 Pascale Cloastre 1, 2
1 Laboratoire en sciences et techniques de l'information, de la communication et de la connaissance
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
2 Lab-STICC_UBO_MOM_PIM
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance, UBO - Université de Brest
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. 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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Noël Tanguy, Nadia Iassamen, Mihai Telescu, Pascale Cloastre. Parameter optimization of orthonormal basis functions for efficient rational approximations. Applied Mathematical Modelling, Elsevier, 2015, 39, pp.4963-4970. ⟨10.1016/j.apm.2015.04.017⟩. ⟨hal-01160320⟩

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