Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 239703, 10 pages
http://dx.doi.org/10.1155/2013/239703
Research Article

Piecewise Bivariate Hermite Interpolations for Large Sets of Scattered Data

1School of Mathematics and Systematic Science, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
2Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing 100191, China

Received 12 January 2013; Accepted 13 March 2013

Academic Editor: Ray K. L. Su

Copyright © 2013 Renzhong Feng and Yanan Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. Xiong, W. Fan, and R. Ding, “Least-squares parameter estimation algorithm for a class of input nonlinear systems,” Journal of Applied Mathematics, vol. 2012, Article ID 684074, 14 pages, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. F. Ding, H. Chen, and M. Li, “Multi-innovation least squares identification methods based on the auxiliary model for MISO systems,” Applied Mathematics and Computation, vol. 187, no. 2, pp. 658–668, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. F. Ding, P. X. Liu, and G. Liu, “Multi-innovation least-squares identification for system modeling,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 40, no. 3, pp. 767–778, 2010. View at Publisher · View at Google Scholar
  4. R. Z. Feng and R. H. Wang, “Closed smooth surface defined from cubic triangular splines,” Journal of Computational Mathematics, vol. 23, no. 1, pp. 67–74, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. R. Z. Feng and R. H. Wang, “Smooth spline surfaces over arbitrary topological triangular meshes,” Journal of Software, vol. 14, no. 4, pp. 830–837, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. Lee, Ge. Wolberg, and S. Y. Shin, “Scattered data interpolation with multilevel B-splines,” IEEE Transactions on Visualization and Computer Graphics, vol. 3, no. 3, pp. 228–244, 1997. View at Publisher · View at Google Scholar
  7. W. Z. Xu, L. T. Guan, and Y. X. Xu, “Smoothing of space scattered data by polynomial natural splines,” Acta Scientiarum Naturalium Universitatis Sunyatseni, vol. 49, no. 6, pp. 20–30, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Z. M. Wu, “Radial basis functions in scattered data interpolation and the meshless method of numerical solution of PDEs,” Chinese Journal of Engineering Mathematics, vol. 19, no. 2, pp. 1–12, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. D. Lazzaro and L. B. Montefusco, “Radial basis functions for the multivariate interpolation of large scattered data sets,” Journal of Computational and Applied Mathematics, vol. 140, no. 1-2, pp. 521–536, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. R. Feng and L. Xu, “Large scattered data fitting based on radial basis functions,” Computer Aided Drafting, Design and Manufacturing, vol. 17, no. 1, pp. 66–72, 2007. View at Google Scholar
  11. R. Franke and H. Hagen, “Least squares surface approximation using multiquadrics and parametric domain distortion,” Computer Aided Geometric Design, vol. 16, no. 3, pp. 177–196, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. T. Sauer and Y. Xu, “On multivariate Hermite interpolation,” Advances in Computational Mathematics, vol. 4, no. 3, pp. 207–259, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Z. M. Wu, “Hermite-Birkhoff interpolation of scattered data by radial basis functions,” Approximation Theory and Its Applications, vol. 8, no. 2, pp. 1–10, 1992. View at Google Scholar · View at MathSciNet
  14. L. Zha and R. Feng, “A scattered hermite interpolation using radial basis Functions,” Journal of Information Computational Science, vol. 4, pp. 361–369, 2007. View at Google Scholar
  15. B. Delaunay, “Sur la sphère vide,” Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskikh i Estestvennykh Nauk, vol. 7, pp. 793–800, 1934. View at Google Scholar
  16. R. Franke and G. Nielson, “Smooth interpolation of large sets of scattered data,” International Journal for Numerical Methods in Engineering, vol. 15, no. 11, pp. 1691–1704, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. D. Shepard, “A two-dimensional interpolation function for irregularly spaced data,” in Proceedings of the 23rd ACM National Conference, pp. 517–524, ACM, 1968. View at Publisher · View at Google Scholar