Optimal Partitioning of Newton's Method for Calculating Roots.

Abstract

In this paper an algorithm for calculating roots is given that is Newton's method initialized with a piecewise best starting approximation. The piecewise best starting approximation corresponds to a partition of the interval of the domain of Newton's method and it is shown how to choose this partition to be optimal. Explicit formulas are given when linear polynomials are used for the best starting approximations. Specific examples are given for square roots, cube roots and reciprocal square roots. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1977
Accession Number
ADA046457

Entities

People

  • Gerald D. Taylor
  • Guenter Meinardus

Organizations

  • Colorado State University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Algorithms
  • Colorado
  • Computers
  • Equations
  • Errors
  • Inequalities
  • Intervals
  • Iterations
  • Mathematics
  • Numbers
  • Polynomials
  • Real Numbers
  • Square Roots
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Fluid Dynamics.