, Volume 45, Issue 2, pp 95–117 | Cite as

Systolic computation of interpolating polynomials

  • P. R. Cappello
  • E. Gallopoulos
  • Ç. K. Koç


Several time-optimal and spacetime-optimal systolic arrays are presented for computing a process dependence graph corresponding to the Aitken algorithm. It is shown that these arrays also can be used to compute the generalized divided differences, i.e., the coefficients of the Hermite interpolating polynomial. Multivariate generalized divided differences are shown to be efficiently computed on a 2-dimensional systolic array. The techniques also are applied to the Neville algorithm, producing similar results.

AMS Subject Classifications

65D05 68Q80 68N99 

Key words

Newton interpolation Hermite interpolation Aitken's algorithm Neville's algorithm systolic array 

Systolische Berechnung von interpolierenden Polynomen


Zur Berechnung eines zum Aitken-Algorithmus gehörigen Prozeßabhängigkeitsgraphen werden einige Zeit-optimale und Raum-Zeit-optimale systolische Felder vorgestellt. Es wird gezeigt, daß man diese Felder auch zur Berechnung verallgemeinerter dividierter Differenzen verwenden kann, wie sie als Koeffizienten des Hermiteschen Interpolationspolynoms auftreten. Die effiziente Berechnung multivariater verallgemeinerter dividierter Differenzen auf einem zweidimensionalen systolischen Feld wird gezeigt. Für den Neville-Algorithmus ergeben die Techniken ähnliche Ergebnisse.


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • P. R. Cappello
    • 1
  • E. Gallopoulos
    • 2
  • Ç. K. Koç
    • 3
  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Center for Super computing Research and DevelopmentUniversity of Illinois at Urbana ChampaignUrbanaUSA
  3. 3.Department of Electrical EngineeningUniversity of HoustonHoustonUSA

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