Optimal starting values for Newton-Raphson calculation of √x ½
David G. Moursund · Communications of the ACM · 1967
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.