Comparison of Different Radial Basis Functions in Dynamical Systems

Carlos Argáez; Peter Giesl; Sigurdur Hafstein

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Paper

Comparison of Different Radial Basis Functions in Dynamical Systems

Topics: Computer Simulation Techniques; Dynamical Systems Models and Methods; Mathematical Simulation; Non-Linear Systems

In Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications SIMULTECH - Volume 1, 394-405, 2021

Authors: Carlos Argáez ¹ ; Peter Giesl ² and Sigurdur Hafstein ¹

Affiliations: ¹ Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavík, Iceland ; ² Department of Mathematics, University of Sussex, Falmer, BN1 9QH, U.K.

Keyword(s): Generalised Interpolation, Radial Basis Functions, Complete Lyapunov Functions.

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 Matérn kernels ψ(n+3)/2 and ψ(n+5)/2.

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Paper citation in several formats:

Argáez, C.; Giesl, P. and Hafstein, S. (2021). Comparison of Different Radial Basis Functions in Dynamical Systems. In Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - SIMULTECH; ISBN 978-989-758-528-9; ISSN 2184-2841, SciTePress, pages 394-405. DOI: 10.5220/0010575203940405

@conference{simultech21,
author={Carlos Argáez. and Peter Giesl. and Sigurdur Hafstein.},
title={Comparison of Different Radial Basis Functions in Dynamical Systems},
booktitle={Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - SIMULTECH},
year={2021},
pages={394-405},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0010575203940405},
isbn={978-989-758-528-9},
issn={2184-2841},
}

TY - CONF

JO - Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - SIMULTECH
TI - Comparison of Different Radial Basis Functions in Dynamical Systems
SN - 978-989-758-528-9
IS - 2184-2841
AU - Argáez, C.
AU - Giesl, P.
AU - Hafstein, S.
PY - 2021
SP - 394
EP - 405
DO - 10.5220/0010575203940405
PB - SciTePress