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Computing

, Volume 53, Issue 3–4, pp 233–242 | Cite as

Optimal initial approximations for the Newton-Raphson division algorithm

  • M. J. Schulte
  • J. Omar
  • E. E. SwartzlanderJr.
Article

Abstract

Newton-Raphson iteration provides a high-speed method for performing division. The Newton-Raphson division algorithm begins with an initial approximation to the reciprocal of the divisor. This value is iteratively refined until a specified accuracy is achieved. In this paper, we develop methods for selecting constant and linear approximations which minimize the maximum absolute error of the final result. These approximations are compared with previous methods which minimize the maximum relative error in the final result or the maximum absolute error in the initial value.

AMS Subject Classification

65D15 

Key words

Division Newton-Raphson initial approximation relative error absolute error error analysis computer arithmetic 

Optimale Anfangsnäherungen für den Newton-Raphson Divisionsalgorithmus

Zusammenfassung

Die Newton-Raphson Iteration, die eine schnelle Division gestattet, beginnt mit einer Anfangsnäherung für den Kehrwert des Divisors. Dieser Wert wird iterativ verbessert, bis die vorgegebene Genauigkeit erreicht ist. In der Arbeit wird die Auswahl von konstanten und linearen Näherungen beschrieben, die den maximalen Absolutfehler des Endergebnisses minimieren. Diese Näherungen werden mit vorliegenden Verfahren verglichen, bei denen der maximale Relativfehler im Endergebnis oder der maximale Absolutfehler der Anfangsnäherung minimiert wird.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • M. J. Schulte
    • 1
  • J. Omar
    • 1
  • E. E. SwartzlanderJr.
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of Texas at AustinAustinUSA

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