, Volume 30, Issue 2, pp 268–288

A parallel method for fast and practical high-order newton interpolation

Part II Numerical Mathematics

DOI: 10.1007/BF02017348

Cite this article as:
EĞecioĞlu, Ö., Gallopoulos, E. & Koç, Ç.K. BIT (1990) 30: 268. doi:10.1007/BF02017348


We present parallel algorithms for the computation and evaluation of interpolating polynomials. The algorithms use parallel prefix techniques for the calculation of divided differences in the Newton representation of the interpolating polynomial. Forn+1 given input pairs, the proposed interpolation algorithm requires only 2 [log(n+1)]+2 parallel arithmetic steps and circuit sizeO(n2), reducing the best known circuit size for parallel interpolation by a factor of logn. The algorithm for the computation of the divided differences is shown to be numerically stable and does not require equidistant points, precomputation, or the fast Fourier transform. We report on numerical experiments comparing this with other serial and parallel algorithms. The experiments indicate that the method can be very useful for very high-order interpolation, which is made possible for special sets of interpolation nodes.

AMS Subject Classifications (1985)

65D05 65W05 68C25 

Copyright information

© BIT Foundations 1990

Authors and Affiliations

  • Ö. EĞecioĞlu
    • 1
    • 2
  • E. Gallopoulos
    • 1
    • 2
  • Ç. K. Koç
    • 3
  1. 1.Department of Computer ScienceUniversity of California Santa BarbaraSanta BarbaraUSA
  2. 2.Center for Supercomputing Research and Development and Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  3. 3.Department of Electrical EngineeringUniversity of HoustonHoustonUSA

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