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Systolic computation of interpolating polynomials

Systolische Berechnung von interpolierenden Polynomen

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Abstract

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.

Zusammenfassung

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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Additional information

This work was supported in part by the Office of Naval Research under contracts N00014-84-K-0664 and N00014-85-K-0553.

Supported by the National Science Foundation under Grants Nos. US NSF-MIP-8410110, US NSF DCR85-09970, and US NSF CCR-8717942, and by AT&T Grant AT&T AFFL67Sameh.

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Cappello, P.R., Gallopoulos, E. & Koç, Ç.K. Systolic computation of interpolating polynomials. Computing 45, 95–117 (1990). https://doi.org/10.1007/BF02247877

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AMS Subject Classifications

  • 65D05
  • 68Q80
  • 68N99

Key words

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