From: Francesco Potorti` <pot@gnu.org>
To: gsl-discuss@sources.redhat.com
Subject: Root finding page manual suggestion
Date: Wed, 19 Dec 2001 13:20:00 -0000 [thread overview]
Message-ID: <E15uDcB-00021q-00@pot.cnuce.cnr.it> (raw)
In the "Root Finding Algorithms using Derivatives" page one reads that
the Newton's method converges quadratically for single roots, while the
secant method has 1.6 convergence order, and "can be useful when
computation of the derivative is costly".
In fact, as far as I know, it is almost always preferable to Newton's
method.
Quoting from "Numerical Methods" by Germund Dahlquist and Ake Bjorck,
translated by Ned Anderson - Prentice-Hall Inc., 1974.
Chapter 6.4.1. (the end) pg 229
The choice between the secant method and Newton-Raphson's method
depends on the amount of work required to compute f'(x). Suppose the
amount of work to compute f'(x) is T times the amount of work to
compute a value of f(x). Then an asymptotic analysis can be used to
motivate the rule: if T > 0.44, then use the secant method; otherwise,
use Newton-Raphson's method.
I've used this criterion in some small numerical program I've written,
and it works ok. The above means that Newton's method wins only if
computing f'(x) is more than twice faster than computing f(x), a quite
rare occurrence in practice. I suggest this fact to be mentioned in the
manual.
Please Cc to me while replying, as I am not subscribed to the list.
next reply other threads:[~2001-12-19 13:20 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
2001-12-19 13:20 Francesco Potorti` [this message]
2001-12-19 13:20 ` Jonathan Leto
2001-12-19 13:20 ` Brian Gough
2001-12-19 13:20 Mikael Adlers
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=E15uDcB-00021q-00@pot.cnuce.cnr.it \
--to=pot@gnu.org \
--cc=gsl-discuss@sources.redhat.com \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for read-only IMAP folder(s) and NNTP newsgroup(s).