Optimal partitioning of Newton's method for calculating roots

Authors:
Günter Meinardus and G. D. Taylor

Journal:
Math. Comp. **35** (1980), 1221-1230

MSC:
Primary 65H05; Secondary 41A30

DOI:
https://doi.org/10.1090/S0025-5718-1980-0583499-5

MathSciNet review:
583499

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Abstract: In this paper, an algorithm is given for calculating roots via Newton's method initialized with a piecewise best starting approximation. The piecewise best starting approximation corresponds to an optimal partitioning of the interval of the domain of Newton's method. Explicit formulas are given when piecewise linear polynomials are used for the best starting approximations. Specific tables are given for square roots, cube roots and reciprocal square roots.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1980-0583499-5

Keywords:
Computation of roots,
optimal initialization of Newton's method for computing roots,
best piecewise starting approximations

Article copyright:
© Copyright 1980
American Mathematical Society