Accession Number:

ADA046457

Title:

Optimal Partitioning of Newton's Method for Calculating Roots.

Descriptive Note:

Interim rept.,

Corporate Author:

COLORADO STATE UNIV FORT COLLINS DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

1977-05-01

Pagination or Media Count:

22.0

Abstract:

In this paper an algorithm for calculating roots is given that is Newtons method initialized with a piecewise best starting approximation. The piecewise best starting approximation corresponds to a partition of the interval of the domain of Newtons 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

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE