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Automatic errorbounds for the approximate solution of equations

Automatische Fehlerschranken für Näherungslösungen von Gleichungen

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Summary

Interval arithmetic is used to obtain errorbounds for alleged solutions of scalar and operator equations. These bounds are derived from theCauchy-Ostrowski-Kantorovich analysis ofNewtons method and can be implemented on a digital computer. It is clained that the method can be fully automated and used in devising general purpose programs for the solution of equations.

Zusammenfassung

Man benutzt Intervallarithmetik um Fehlerabschätzungen für Näherungslösungen von Skalar- und Operatorgleichungen zu bekommen. Diese Abschätzungen werden aus den Arbeiten vonCauchy-Ostrowski-Kantorovich über dasNewtonsche Verfahren abgeleitet. Wir behaupten, daß das Verfahren völlig automatisiert werden kann und daß es für die Herleitung allgemeiner Programme für die Lösung von Gleichungen benutzt werden kann.

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References

  1. Lancaster, P.: Error Analysis for theNewton-Raphson Method. NM9, 55 (1966).

    Google Scholar 

  2. Wilkinson, J. H.: Rounding Errors in Algebraic Processes. Englewood Cliffs, N. J.: Prentice Hall. 1963.

    Google Scholar 

  3. Nickel, K., N. Apostolatos andU. Kulisch: Ein Einschließungsverfahren für Nullstellen. Comp.2, 3, 195 (1967).

    Google Scholar 

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

    Google Scholar 

  5. Dwyer, P.: Linear Computations. New York: John Wiley & Sons Inc. 1951.

    Google Scholar 

  6. Apostolatos, N., undU. Kulisch: Grundlagen einer Maschinenintervallarithmetik. Comp.2, 1, 89 (1967).

    Google Scholar 

  7. Apostolatos, N., undU. Kulisch: Approximation der erweiterten Intervallarithmetik durch die einfache Maschinenintervallarithmetik. Comp.2, 3, 181 (1967).

    Google Scholar 

  8. Ostrowski, A. M.: Solution of Equations and Systems of Equations. New York: Academic Press. 1966.

    Google Scholar 

  9. Champagne, W. P., J. R.: On Finding Roots of Polynomials by Hook or by Crook. TTN-37, The University of Texas, Computation Center. 1964.

  10. Nickel, K.: Die numerische Berechnung der Wurzeln eines Polynoms. NM9, 80 (1966).

    Google Scholar 

  11. Kantorovich, L. V., andG. P. Akilov: Functional Analysis in Normed Spaces. Oxford: Pergamon Press Ltd. 1964.

    Google Scholar 

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Author information

Author notes

  1. J. Rokne

    Present address: Department of Matheamtics, The University of Calgary, Calgary 44, Alberta, Canada

Authors and Affiliations

  1. Department of Mathematics, The University of Basel, Rheinsprung 21, CH-4000, Basel, Switzerland

    J. Rokne &  P. Lancaster

  2. Department of Mathematics, The University of Calgary, Alberta, Canada

    P. Lancaster

Authors
  1. J. Rokne
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  2. P. Lancaster
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Rokne, J., Lancaster, P. Automatic errorbounds for the approximate solution of equations. Computing 4, 294–303 (1969). https://doi.org/10.1007/BF02235464

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  • DOI: https://doi.org/10.1007/BF02235464

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