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Home → Magazine Archive → July 1967 (Vol. 10, No. 7) → A language independent macro processor → Abstract

A language independent macro processor

By William M. Waite

Communications of the ACM, Vol. 10 No. 7, Pages 433-440
10.1145/363427.363458

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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