Skip to main content
Log in

Explicit calculation of the Lagrangian interval interpolating polynomial

Explizite Berechnung des Lagrangeschen Intervallinterpolationspolynoms

  • Published:
Computing Aims and scope Submit manuscript

Summary

Three algorithms for calculating the explicit Lagrange interval interpolating polynomial are discussed, one of which is shown to be superior to the other two. The algorithms were tested on several examples.

Zusammenfassung

Drei Algorithmen für die Berechnung des expliziten Lagrange-Intervall-Interpolationspolynoms werden untersucht. Es wird gezeigt, daß eine dieser drei Methoden besser ist als die anderen zwei. Die Algorithmen wurden mit vielen Beispielen getestet.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Apostolatos, N., undV. Kulisch: Grundlagen einer Maschinenintervallarithmetik. Comp.2, 89 (1968).

    Google Scholar 

  2. Apostolatos, N., andV. Kulisch: Approximation der erweiterten Intervallarithmetik durch die einfache Maschinenintervallarithmetik. Comp.2, 181 (1968).

    Google Scholar 

  3. Gibb, A.: Procedures for Range Arithmetic, Algorithm 61. Comm. ACM4, 319 (1961).

    Google Scholar 

  4. Krawczyk, R.: Iterationsverfahren zur Bestimmung komplexer Nullstellen. Interner Bericht Nr. 4, Inst. für Informatik, University of Karlsruhe.

  5. Krogh, F. T.: Efficient Algorithms for Polynomial Interpolation and Numerical Differentiation. Math. Comp.24, 185–190 (1970).

    Google Scholar 

  6. Marden, M.: Geometry of Polynomials. Mathematical Surveys No. 3, Amer. Math. Soc., Providence (R.I.)

  7. Moore, R.: Interval Analysis. Englewood Cliffs, N. J.: Prentice Hall. 1966.

    Google Scholar 

  8. Moore, R.: Practical Aspects of Interval Computation. Aplikace Mathematiky1968, 53–92.

  9. Newbery, A. C. C.: Interpolation by Algebraic and Trigonometric Polynomials. Math. Comp. V.20, 597–599 (1966). MR 34 No. 3752.

    Google Scholar 

  10. Rokne, J.: Interval Arithmetic for CDC 6400 FTN (Manuscript).

  11. Wippermann, H. W.: Realisierung einer Intervall-Arithmetik in einem ALGOL-60-System. Elektronische Rechenanl.9, 224 (1967).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rokne, J. Explicit calculation of the Lagrangian interval interpolating polynomial. Computing 9, 149–157 (1972). https://doi.org/10.1007/BF02236964

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02236964

Keywords

Navigation