Newton and Halley's methods with enhanced derivatives estimation

[Gerson W. Barbosa]

(10-06-2017 07:27 PM)Dieter Wrote:  In your example for a 12-digit machine I would try T=1E–8. Could you give it a try and see how well the returned solution agrees with the true result? Maybe after one additional final iteration?

T = 1E-8

Initial guess: 0.1

0.0659646010039

After one additional iteration:

0.0659646009050

Exact 12-digit result:

0.0659646009778

Thank you very much for your valuable lessons!

Gerson.