By David G. Moursund
Communications of the ACM,
Vol. 10 No. 7, Pages 430-432
The problem of obtaining starting values for the Newton-Raphson calculation of √x on a digital computer is considered. It is shown that the conventionally used best uniform approximations to √x do not provide optimal starting values. The problem of obtaining optimal starting values is stated, and several basic results are proved. A table of optimal polynomial starting values is given.
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