Improved Newton iteration for integral roots
Author:
Richard F. King
Journal:
Math. Comp. 25 (1971), 299-304
MSC:
Primary 65.50
DOI:
https://doi.org/10.1090/S0025-5718-1971-0283981-9
MathSciNet review:
0283981
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Abstract | References | Similar Articles | Additional Information
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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Additional Information
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
