Starting approximations for square root calculation on IBM system /360
Communications of the ACM
Proceedings of the 1999 ACM symposium on Applied computing
On an algorithm for nonlinear minimax approximation
Communications of the ACM
Optimal starting approximations for generating square root for slow or no divide
Communications of the ACM
The logarithmic error and Newton's method for the square root
Communications of the ACM
Improvements based on computed errors
Communications of the ACM
A rational approximation optimal by Moursund's criterion
Communications of the ACM
Evaluation of the square root function on microprocessors
ACM '76 Proceedings of the 1976 annual conference
Choosing starting values for certain Newton-Raphson iterations
Theoretical Computer Science - Real numbers and computers
Establishing lower bounds on algorithms: a survey
AFIPS '72 (Spring) Proceedings of the May 16-18, 1972, spring joint computer conference
Hi-index | 48.30 |
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.