Comparison of different radial basis functions in dynamical systems

Argáez; Peter Giesl; Sigurdur Hafstein

doi:10.5220/0010575203940405

Comparison of different radial basis functions in dynamical systems

Argáez, Peter Giesl, Sigurdur Hafstein

Faculty of Physical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper we study the impact of using different radial basis functions for the computation of complete Lyapunov function candidates using generalised interpolation. We compare the numerical well-posedness of the discretised problem, condition numbers of the collocation matrices, and the quality of the solutions for Wendland functions ψ_3,1 and ψ_5,3, Gaussians, Inverse quadratics and Inverse multiquadrics, and Matérn kernels ψ₍n+3)/₂ and ψ₍n+5)/2.

Original language	English
Title of host publication	Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021
Editors	Gerd Wagner, Frank Werner, Tuncer Oren, Floriano De Rango
Publisher	SciTePress
Pages	394-405
Number of pages	12
ISBN (Electronic)	9789897585289
DOIs	https://doi.org/10.5220/0010575203940405
Publication status	Published - 1 Jan 2021
Event	11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021 - Virtual, Online Duration: 7 Jul 2021 → 9 Jul 2021

Publication series

Name	Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021

Conference

Conference	11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021
City	Virtual, Online
Period	7/07/21 → 9/07/21

Bibliographical note

Publisher Copyright:
Copyright © 2021 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved.

Other keywords

Complete Lyapunov Functions
Generalised Interpolation
Radial Basis Functions

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10.5220/0010575203940405

Cite this

Argáez, Giesl, P., & Hafstein, S. (2021). Comparison of different radial basis functions in dynamical systems. In G. Wagner, F. Werner, T. Oren, & F. De Rango (Eds.), Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021 (pp. 394-405). (Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021). SciTePress. https://doi.org/10.5220/0010575203940405

Argáez ; Giesl, Peter ; Hafstein, Sigurdur. / Comparison of different radial basis functions in dynamical systems. Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021. editor / Gerd Wagner ; Frank Werner ; Tuncer Oren ; Floriano De Rango. SciTePress, 2021. pp. 394-405 (Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021).

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abstract = "In this paper we study the impact of using different radial basis functions for the computation of complete Lyapunov function candidates using generalised interpolation. We compare the numerical well-posedness of the discretised problem, condition numbers of the collocation matrices, and the quality of the solutions for Wendland functions ψ3,1 and ψ5,3, Gaussians, Inverse quadratics and Inverse multiquadrics, and Mat{\'e}rn kernels ψ(n+3)/2 and ψ(n+5)/2.",

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author = "Arg{\'a}ez and Peter Giesl and Sigurdur Hafstein",

note = "Publisher Copyright: Copyright {\textcopyright} 2021 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved.; 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021 ; Conference date: 07-07-2021 Through 09-07-2021",

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Argáez, Giesl, P & Hafstein, S 2021, Comparison of different radial basis functions in dynamical systems. in G Wagner, F Werner, T Oren & F De Rango (eds), Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021. Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021, SciTePress, pp. 394-405, 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021, Virtual, Online, 7/07/21. https://doi.org/10.5220/0010575203940405

Comparison of different radial basis functions in dynamical systems. / Argáez; Giesl, Peter; Hafstein, Sigurdur.
Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021. ed. / Gerd Wagner; Frank Werner; Tuncer Oren; Floriano De Rango. SciTePress, 2021. p. 394-405 (Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Argáez, Giesl P, Hafstein S. Comparison of different radial basis functions in dynamical systems. In Wagner G, Werner F, Oren T, De Rango F, editors, Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021. SciTePress. 2021. p. 394-405. (Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021). doi: 10.5220/0010575203940405

Comparison of different radial basis functions in dynamical systems

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