Best rational starting approximations and improved Newton iteration for the square root

Author:
Ichizo Ninomiya

Journal:
Math. Comp. **24** (1970), 391-404

MSC:
Primary 65.50

DOI:
https://doi.org/10.1090/S0025-5718-1970-0273809-4

MathSciNet review:
0273809

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Abstract | References | Similar Articles | Additional Information

Abstract: The most important class of the best rational approximations to the square root is obtained analytically by means of elliptic function theory. An improvement of the Newton iteration procedure is proposed.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0273809-4

Keywords:
Rational approximation,
best approximation,
square root,
Newton iteration,
starting approximation,
Chebyshev's criterion,
Moursund's criterion,
logarithmic criterion,
Jacobian elliptic function,
transformation of elliptic functions

Article copyright:
© Copyright 1970
American Mathematical Society