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author | James LewisMoss <dres@debian.org> | 2001-07-27 23:45:29 -0400 |
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committer | Bryan Newbold <bnewbold@robocracy.org> | 2017-02-20 00:05:29 -0800 |
commit | f559c149c83da84d0b1c285f0298c84aec564af9 (patch) | |
tree | f1c91bcb9bb5e6dad87b643127c3f878d80d89ee /minimize.txi | |
parent | c394920caedf3dac1981bb6b10eeb47fd6e4bb21 (diff) | |
parent | 87b82b5822ca54228cfa6df29be3ad9d4bc47d16 (diff) | |
download | slib-f559c149c83da84d0b1c285f0298c84aec564af9.tar.gz slib-f559c149c83da84d0b1c285f0298c84aec564af9.zip |
Import Debian changes 2d2-1debian/2d2-1
slib (2d2-1) unstable; urgency=low
* New upstream version
* Revert back to free. Is now so.
slib (2d1-1) unstable; urgency=low
* New upstream version.
* Move to non-free. FSF pointed out license doesn't allow modified
versions to be distributed.
* Get a complete list of copyrights that apply to the source into
copyright file.
* Remove setup for guile 1.3.
* Remove postrm. Just calling install-info (lintian) Move install-info
call to prerm since doc-base doesn't do install-info.
slib (2c9-3) unstable; urgency=low
* Change info location to section "The Algorithmic Language Scheme" to
match up with where guile puts it's files.
* Postinst is running slibconfig now. (Closes: #75891)
slib (2c9-2) unstable; urgency=low
* Stop installing slibconfig (for guile).
* In postinst if /usr/sbin/slibconnfig exists call it (Close: #75843
#75891).
slib (2c9-1) unstable; urgency=low
* New upstream (Closes: #74760)
* replace string-index with strsrch:string-index in http-cgi.scm.
* Add doc-base support (Closes: #31163)
Diffstat (limited to 'minimize.txi')
-rw-r--r-- | minimize.txi | 48 |
1 files changed, 48 insertions, 0 deletions
diff --git a/minimize.txi b/minimize.txi new file mode 100644 index 0000000..785be35 --- /dev/null +++ b/minimize.txi @@ -0,0 +1,48 @@ +@noindent + +The Golden Section Search +@footnote{David Kahaner, Cleve Moler, and Stephen Nash +@cite{Numerical Methods and Software} +Prentice-Hall, 1989, ISBN 0-13-627258-4} +algorithm finds minima of functions which +are expensive to compute or for which derivatives are not available. +Although optimum for the general case, convergence is slow, +requiring nearly 100 iterations for the example (x^3-2x-5). + +@noindent + +If the derivative is available, Newton-Raphson is probably a better +choice. If the function is inexpensive to compute, consider +approximating the derivative. + + +@defun golden-section-search f x0 x1 prec + + +@var{x_0} are @var{x_1} real numbers. The (single argument) +procedure @var{f} is unimodal over the open interval (@var{x_0}, +@var{x_1}). That is, there is exactly one point in the interval for +which the derivative of @var{f} is zero. + +@code{golden-section-search} returns a pair (@var{x} . @var{f}(@var{x})) where @var{f}(@var{x}) +is the minimum. The @var{prec} parameter is the stop criterion. If +@var{prec} is a positive number, then the iteration continues until +@var{x} is within @var{prec} from the true value. If @var{prec} is +a negative integer, then the procedure will iterate @var{-prec} +times or until convergence. If @var{prec} is a procedure of seven +arguments, @var{x0}, @var{x1}, @var{a}, @var{b}, @var{fa}, @var{fb}, +and @var{count}, then the iterations will stop when the procedure +returns @code{#t}. + +Analytically, the minimum of x^3-2x-5 is 0.816497. +@example +(define func (lambda (x) (+ (* x (+ (* x x) -2)) -5))) +(golden-section-search func 0 1 (/ 10000)) + ==> (816.4883855245578e-3 . -6.0886621077391165) +(golden-section-search func 0 1 -5) + ==> (819.6601125010515e-3 . -6.088637561916407) +(golden-section-search func 0 1 + (lambda (a b c d e f g ) (= g 500))) + ==> (816.4965933140557e-3 . -6.088662107903635) +@end example +@end defun |