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Mathematics of Computation

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Improved Newton iteration for integral roots


Author: Richard F. King
Journal: Math. Comp. 25 (1971), 299-304
MSC: Primary 65.50
MathSciNet review: 0283981
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Abstract: An improved Newton iteration procedure for computing pth roots from best Chebyshev or Moursund initial approximations is developed. It differs from the usual Newton method by a multiplicative factor at each step. This multiplier halves the relative error by translating the usual one-sided error curve into a two-sided one, and then adjusting to make a Moursund-like fit. The generalized logarithmic error is used in determining this set of factors.


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DOI: https://doi.org/10.1090/S0025-5718-1971-0283981-9
Keywords: Newton's method, integral root, generalized logarithmic error, one-sided error, Moursund approximation, best rational fit, Chebyshev-like error, improvement factors, convergence rate
Article copyright: © Copyright 1971 American Mathematical Society