Optimal Starting Values for Newton-Raphson Calculation of SQRT(x) The problem of obtaining starting values for the Newton-Raphson calculation of SQRT(x) on a digital computer is considered. It is shown that the conventionally used best uniform approximations to SQRT(x) do not provide optimal starting values. The problem of obtaining 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. CACM July, 1967 Moursund, D. G. CA670707 JB February 28, 1978 8:53 AM 1566 4 1566 1440 5 1566 1566 5 1566 1566 5 1566 1566 5 1566 1932 5 1566 2094 5 1566 962 6 1566 1566 6 1566 1566 6 1566