Advertisement

Speedup of Bicubic Spline Interpolation

  • Viliam Kačala
  • Csaba Török
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10861)

Abstract

The paper seeks to introduce a new algorithm for computation of interpolating spline surfaces over non-uniform grids with \(C^2\) class continuity, generalizing a recently proposed approach for uniform grids originally based on a special approximation property between biquartic and bicubic polynomials. The algorithm breaks down the classical de Boor’s computational task to systems of equations with reduced size and simple remainder explicit formulas. It is shown that the original algorithm and the new one are numerically equivalent and the latter is up to 50% faster than the classic approach.

Keywords

Bicubic spline Hermite spline Spline interpolation Speedup Tridiagonal systems 

Notes

Acknowledgements

This work was partially supported by projects Technicom ITMS 26220220182 and APVV-15-0091 Effective algorithms, automata and data structures.

References

  1. 1.
    Björck, A.: Numerical Methods in Matrix Computations. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-319-05089-8CrossRefzbMATHGoogle Scholar
  2. 2.
    de Boor, C.: Bicubic spline interpolation. J. Math. Phys. 41(3), 212–218 (1962)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Intel 64 and IA-32 Architectures Optimization Reference Manual. Intel Corp., C-5-C-16 (2016). http://www.intel.com/content/dam/www/public/us/en/documents/manuals/64-ia-32-architectures-optimization-manual.pdf
  4. 4.
    Kačala, V., Miňo, L.: Speeding up the computation of uniform bicubic spline surfaces. Com. Sci. Res. Not. 2701, 73–80 (2017)Google Scholar
  5. 5.
    Kačala, V., Miňo, L., Török, Cs.: Enhanced speedup of uniform bicubic spline surfaces. ITAT 2018, to appearGoogle Scholar
  6. 6.
    Miňo, L., Török, Cs.: Fast algorithm for spline surfaces. Communication of the Joint Institute for Nuclear Research, Dubna, Russia, E11–2015-77, pp. 1–19 (2015)Google Scholar
  7. 7.
    Patterson, J.R.C.: Modern Microprocessors - A 90-Minute Guide!, Lighterra (2015)Google Scholar
  8. 8.
    Török, Cs.: On reduction of equations’ number for cubic splines. Matematicheskoe modelirovanie, 26(11) (2014)Google Scholar
  9. 9.
    Software Optimization Guide for AMD Family 10h and 12h Processors. Advanced Micro Devices Inc., pp. 265–279 (2011). http://support.amd.com/TechDocs/40546.pdf
  10. 10.
    Software Optimization Guide for AMD Family 15h Processors. Advanced Micro Devices Inc., pp. 265–279 (2014). http://support.amd.com/TechDocs/40546.pdf

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.P. J. Šafárik University in KošiceKošiceSlovakia

Personalised recommendations