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Hermite interpolation of multivariable function given at scattered points

Publication date: 25.08.2017

Technical Transactions, 2017, Volume 8 Year 2017 (114), pp. 199-205

https://doi.org/10.4467/2353737XCT.17.142.6893

Authors

,
Artur Krowiak
Institute of Applied Informatics, Faculty of Mechanical Engineering, Cracow University of Technology
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Jordan Podgórski
Cracow University of Technology
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Hermite interpolation of multivariable function given at scattered points

Abstract

The paper shows the approach to the interpolation of scattered data which includes not only function values, but also values of derivatives of the function. To this end, an interpolant composed of radial basis functions is used and extended by terms possessing appropriate derivative terms. The latter match the given derivatives. Special attention is paid to the problem of choosing the value of the shape parameter, which is included in radial functions and influences the accuracy and stability of the solution. To validate the method, several numerical tests are carried out in the paper.

References

[1] Fasshauer G.E., Meshfree Approximation Methods with Matlab, World Scientific Publishing, Singapore 2007.
[2] Belytschko T., Krongauz Y., Organ D., Flrming M., Krysl P., Meshless methods: an overview and recent developments, Computer Methods in Applied Mechanics and Engineering,
Vol. 139, 1996, 3–47.
[3] Liu G.R., Meshlees Methods – Moving beyond the Finite Element Method, CRC Press, Boca Raton, Florida 2003.
[4] Buhmann M.D., Multivariete interpolation using radial basis functions, Ph.D. Dissertation, University of Cambridge, 1989.
[5] Schaback R., Creating surfaces from scattered data using radial basis functions, [in:] M. Dehlan, T. Lyche, L. Schumaker (Eds): Mathematical Methods for Curves and Surfaces, Vanderbilt University Press, Nashville 1995, 477–496.
[6] Wu Z., Hermite–Birkhoff Interpolation of Scattered Data by Radial Basis Functions, Approximation Theory and its Applications, Vol. 8, 1992, 1–10.
[7] Krowiak A., Hermite type radial basis function-based differential quadrature method for higher order equations, Applied Mathematical Modelling, Vol. 40, 2016, 2421–2430.
[8] Krowiak A., On choosing a value of shape parameter in Radial Basis Function collocation methods, Numerical Methods for Partial Differential Equations, submitted for publication.

Information

Information: Technical Transactions, 2017, Volume 8 Year 2017 (114), pp. 199-205

Article type: Original article

Titles:

Polish:

Hermite interpolation of multivariable function given at scattered points

English:

Hermite interpolation of multivariable function given at scattered points

Authors

Institute of Applied Informatics, Faculty of Mechanical Engineering, Cracow University of Technology

Cracow University of Technology

Published at: 25.08.2017

Article status: Open

Licence: None

Percentage share of authors:

Artur Krowiak (Author) - 50%
Jordan Podgórski (Author) - 50%

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Publication languages:

English

Hermite interpolation of multivariable function given at scattered points

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