Improved Newton iteration for integral roots
Author:
Richard F. King
Journal:
Math. Comp. 25 (1971), 299304
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 onesided error curve into a twosided one, and then adjusting to make a Moursundlike fit. The generalized logarithmic error is used in determining this set of factors.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197102839819
PII:
S 00255718(1971)02839819
Keywords:
Newton's method,
integral root,
generalized logarithmic error,
onesided error,
Moursund approximation,
best rational fit,
Chebyshevlike error,
improvement factors,
convergence rate
Article copyright:
© Copyright 1971
American Mathematical Society
