Optimal Partitioning of Newton's Method for Calculating Roots.
COLORADO STATE UNIV FORT COLLINS DEPT OF MATHEMATICS
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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
- Theoretical Mathematics