Abstract
This paper extends a previous work done by the same authors on teaching 1d polynomial interpolation using Mathematica [1] to higher dimensions. In this work, it is intended to simplify the the theoretical discussions in presenting multidimensional interpolation in a classroom environment by employing Mathematica’s symbolic properties. In addition to symbolic derivations, some numerical tests are provided to show the interesting properties of the higher dimensional interpolation problem. Runge’s phenomenon was displayed for 2d polynomial interpolation.
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Yazici, A., Altas, I., Ergenc, T.: Symbolic Interpolation using Mathematica. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2004. LNCS, vol. 3039, pp. 365–370. Springer, Heidelberg (2004)
Reiter, C.A.: Exploring Hermite Interpolation with Mathematica. Primus 2(2), 173–182 (1992)
Kaput, J.: Technology and Mathematics Education. In: Grouws, D.A. (ed.) Handbooks of Research on Mathematics Teaching and Learning, pp. 515–556. MacMillan, New York (1992)
De Boor, C.: A Practical Guide to Splines. Springer, Heidelberg (1978)
Mathews, J.H.: Numerical Methods For Computer Science, and Mathematics. Prentice-Hall International, Englewood Cliffs (1987)
Heath, M.T.: Scientific Computing: An Introductory Survey. McGraw-Hill International Editions, New York (1997)
Linz, P.: Theoretical Numerical Analysis: An Introduction to Advanced Techniques. John-Wiley & Sons, Ltd., West Sussex (1979)
Altas, I., Stephenson, J.W.: Existence of Second Order Discretizations on Irregular Mesh. Appl. Math Lett. 2(4), 315–318 (1989)
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Yazici, A., Altas, I., Ergenc, T. (2005). 2d Polynomial Interpolation: A Symbolic Approach with Mathematica. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424857_49
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DOI: https://doi.org/10.1007/11424857_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25862-9
Online ISBN: 978-3-540-32045-6
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