An Example of Two-Dimensional Interpolation Using a Linear Combination of Bicubic B-Splines

• Autorzy: Rosłoniec S.
• Języki publikacji: EN

Abstrakty

EN

The paper describes how a linear combination of bicubic B-splines can be effectively used in a two-dimensional interpolation. It is assumed that values of a function to be interpolated are evaluated at the uniformly located nodes of a corresponding rectangular grid. All formulae of importance have been derived step by step and are presented in a form convenient for computer implementations. To ensure clarity of considerations a short description of one-dimensional B-spline is also given in Appendix 1. The usefulness of the presented interpolation algorithm has been confirmed by the real engineering example of applications.

Słowa kluczowe

EN

numerical analysis; two-variable interpolation; cubic B-splines

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: International Journal of Electronics and Telecommunications
• Rocznik: 2011
• Tom: Vol. 57, No. 3
• Strony: 293--299
• Opis fizyczny: Bibliogr. 14 poz., wykr.

Twórcy

autor

Rosłoniec S.

• Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warsaw, Poland,

Bibliografia

• [1] H. E. Brenner, „Numerical Solution of TEM - Line Problems Involving Inhomogeneous Media”, IEEE Transactions on Microwave Theory and Techniques, vol. 15, pp. 485 - 487, August 1967.
• [2] H. E. Green, „The Numerical Solution of Some Important Transmission - Line Problems”, IEEE Transactions on Microwave Theory and Techniques, vol. 13, pp. 676 - 692, September 1965.
• [3] S. Rosłoniec, Algorithms for Computer-aided Design of Linear Microwave Circuits. Boston (MA): Artech House Inc., 1990.
• [4] B. C. Wadell, Transmission Line Design Handbook. Boston (MA): Artech House Inc., 1991.
• [5] C. Boor, A practical Guide to Splines - Second Edition. New York: Springer-Verlag, 2001.
• [6] J. H. Mathews, Numerical Methods for Mathematics, Science and Engineering. Englewood Cliffs, N. J.: Prentice-Hall International Inc., 1992.
• [7] E. V. Shikin and A. I. Plis, Handbook on Splines for the User. New York: CRC Press, 1995.
• [8] P. Kiciak, Private information of March 17. Warsaw University, Department of Applied Mathematics and Mechanics, 2011.
• [9] S. Rosłoniec, Fundamental Numerical Methods for Electrical Engineering. Heidelberg/Berlin: Springer Verlag, 2008.
• [10] T. A. Davis, Direct Methods for Sparse Linear Systems. Philadelphia ((PA): SIAM Publishing House, 2006.
• [11] I. S. Duff, A. M. Erisman, and J. K. Reid, Direct Methods for Sparse Metrices. Oxford: Oxford University Press, 1989.
• [12] M. A. R. Gunston, Microwave Transmission Line Impedance Data. New York: Van Nostrandt Reinhold Comp., 1972.
• [13] M. V. Schneider, „Computation of Impedance and Attenuation of TEM - Lines by Finite Difference Methods”, IEEE Transactions on Microwave Theory and Techniques, vol. 13, pp. 793 - 800, November 1965.
• [14] M. N. O. Sadiku, Numerical Techniques in Electromagnetics - Second Edition. Boca Raton (Florida), London: CRC Press, 2001.