Newton (Iterative) Vs. Babylonian (Direct) For Roots

Question

Is Newton's iterative method for finding a square root more efficient then the Babylonian method? Considering most roots are irrational, which method would get me within, say 16 decimal places, the fastest? I need a high level of precision so I was curious which would be more efficient.

score 6 · Accepted Answer · answered May 05 '13 at 22:26

6

The Newton-Raphson process for the case of the square root is in effect the same algorithm as the Babylonian Method, aka Heron's Method.

answered May 05 '13 at 22:26

André Nicolas

507,029

score 3 · Answer 2 · answered May 05 '13 at 23:29

3

There are many clever tricks for computing square roots quickly. This is especially true if you really want the reciprocal of a square root, or if you want a square root of the form $\sqrt{ a^2 + b^2}$. See this page, for starters.

answered May 05 '13 at 23:29

bubba

43,483
3
61
122

score 2 · Answer 3 · answered May 05 '13 at 23:06

2

If speed and robustness is key, check Brent's method

answered May 05 '13 at 23:06

vonbrand

27,812

Newton (Iterative) Vs. Babylonian (Direct) For Roots

3 Answers3