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| #! /usr/bin/env python
| import sys
| from typing import Final
|
| n = float(sys.argv[1])
| EPSILON: Final[float] = sys.float_info.epsilon
|
| x = n # !$x_0 = n$!
| while abs(x - (q := n / x)) > (EPSILON * x): # !$\left|\frac{x^2-n}{x^2}\right| > \varepsilon $!
| x = (x + q) / 2.0 # !$x_{i+1} = \frac{1}{2}(x_i + \frac{n}{x_i})$!
|
| print(f"sqrt({n}) ~ {x}")
|
|
