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Hermite interpolation of multivariable function given at scattered points

Data publikacji: 25.08.2017

Czasopismo Techniczne, 2017, Volume 8 Year 2017 (114), s. 199-205

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

Autorzy

,
Artur Krowiak
Institute of Applied Informatics, Faculty of Mechanical Engineering, Cracow University of Technology
Wszystkie publikacje autora →
Jordan Podgórski
Cracow University of Technology
Wszystkie publikacje autora →

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Tytuły

Hermite interpolation of multivariable function given at scattered points

Abstrakt

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.

Bibliografia

[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.

Informacje

Informacje: Czasopismo Techniczne, 2017, Volume 8 Year 2017 (114), s. 199-205

Typ artykułu: Oryginalny artykuł naukowy

Tytuły:

Polski:

Hermite interpolation of multivariable function given at scattered points

Angielski:

Hermite interpolation of multivariable function given at scattered points

Autorzy

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

Cracow University of Technology

Publikacja: 25.08.2017

Status artykułu: Otwarte __T_UNLOCK

Licencja: Żadna

Udział procentowy autorów:

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

Korekty artykułu:

-

Języki publikacji:

Angielski

Hermite interpolation of multivariable function given at scattered points

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