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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.


References [Enhancements On Off] (What's this?)

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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

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