Abstract: "We present parallel algorithms for the computation and evaluation of interpolating polynomials. The algorithms use parallel prefix techniques for the calculations of divided differences in the Newton representation of the interpolating polynomial. For n + 1 given input pairs, the pro...

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Bibliographic Details

Main Authors:	Egecioglu, Omer (Author), Gallopoulos, Efstratios (Author), Koç, Çetin Kaya 1957- (Author)
Format:	Book
Language:	English
Published:	Urbana, Ill. 1989
Series:	Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report 921
Subjects:	Interpolation Parallel processing (Electronic computers)
Summary:	Abstract: "We present parallel algorithms for the computation and evaluation of interpolating polynomials. The algorithms use parallel prefix techniques for the calculations of divided differences in the Newton representation of the interpolating polynomial. For n + 1 given input pairs, the proposed interpolation algorithm requires only 2[log(n+1)]+2 parallel arithmetic steps and circuit size O(n p2 s), reducing the best known circuit size for parallel interpolation by a factor of log n. 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.
Physical Description:	22 S.