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Newton Method
05-15-2016, 02:00 AM (This post was last modified: 05-15-2016 12:23 PM by Namir.)
Post: #10
RE: Newton Method
Hello Dieter,

Last year I was reading "Practical Numerical Methods for Chemical Engineers", third edition, by Richard Davis. When this author discusses Newton's method he uses the following very interesting variant on page 195:

x(i) = x(i-1) - f(x(i-1)) * f'(x(i-1)( / ([f'(x(i-1)]^2 + delta)

Davis uses delta = 1e-5 to protected against the slope f'(x) (approximated using any one of our techniques) being zero. The expression ([f'(x(i-1)]^2 + delta) is always positive.I am guessing that the delta term also stabilizes convergence as f;(x) gets very small too.

The above equation requires a few more calculations and probably one more storage register/variable, but adds more stability.
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Messages In This Thread
Newton Method - bshoring - 05-11-2016, 07:54 PM
RE: Newton Method - Dieter - 05-11-2016, 08:40 PM
RE: Newton Method - Namir - 05-12-2016, 08:47 PM
RE: Newton Method - Dieter - 05-12-2016, 09:17 PM
RE: Newton Method - Namir - 05-13-2016, 01:59 PM
RE: Newton Method - bshoring - 05-14-2016, 07:49 PM
RE: Newton Method - Dieter - 05-14-2016, 10:23 PM
RE: Newton Method - Namir - 05-15-2016 02:00 AM
RE: Newton Method - Dieter - 05-15-2016, 01:11 PM
RE: Newton Method - Namir - 05-15-2016, 01:57 PM
RE: Newton Method - bshoring - 05-12-2016, 12:10 AM
RE: Newton Method - bshoring - 05-14-2016, 06:36 AM
RE: Newton Method - SlideRule - 08-24-2016, 12:08 PM
RE: Newton Method - Pekis - 08-24-2016, 12:20 PM
RE: Newton Method - Csaba Tizedes - 08-24-2016, 08:37 PM
RE: Newton Method - Duane Hess - 08-25-2016, 04:47 AM
RE: Newton Method - Namir - 08-25-2016, 05:00 AM
RE: Newton Method - rprosperi - 08-25-2016, 04:19 PM
RE: Newton Method - bshoring - 08-27-2016, 03:09 AM
RE: Newton Method - Duane Hess - 08-27-2016, 06:31 AM
RE: Newton Method - SlideRule - 08-28-2016, 02:57 AM
RE: Newton Method - rprosperi - 08-29-2016, 12:46 AM



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