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diff scripts/special-matrix/hilb.m @ 12639:4d777e05d47c stable

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doc: Review and update documentation for "Matrix Manipulation" chapter. * matrix.txi, arrayfun.m, blkdiag.m, fliplr.m, flipud.m, logspace.m, postpad.m, prepad.m, randi.m, repmat.m, rot90.m, rotdim.m, shiftdim.m, sortrows.m, vech.m, xor.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, pascal.m, rosser.m, sylvester_matrix.m, toeplitz.m, vander.m, wilkinson.m, bsxfun.cc, find.cc, lookup.cc, rand.cc, tril.cc, data.cc, arrayfun.m, blkdiag.m, fliplr.m, flipud.m, logspace.m, postpad.m, prepad.m, randi.m, repmat.m, rot90.m, rotdim.m, shiftdim.m, sortrows.m, vech.m, xor.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, pascal.m, rosser.m, sylvester_matrix.m, toeplitz.m, vander.m, wilkinson.m, bsxfun.cc (bsxfun), find.cc (find), lookup.cc (lookup), rand.cc (rand, randn, rande, randg, randp), tril.cc (triu), data.cc (all, any, horzcat, vertcat, cat, permute, ipermute, ones, zeros, eye, linspace, resize, reshape, issorted, diff): Improve docstrings
author Rik <octave@nomad.inbox5.com>
date Sun, 01 May 2011 08:55:15 -0700
parents fd0a3ac60b0e
children 779e15b69738
line wrap: on
line diff
--- a/scripts/special-matrix/hilb.m	Tue Apr 26 11:27:28 2011 -0700
+++ b/scripts/special-matrix/hilb.m	Sun May 01 08:55:15 2011 -0700
@@ -18,14 +18,8 @@
 
 ## -*- texinfo -*-
 ## @deftypefn {Function File} {} hilb (@var{n})
-## Return the Hilbert matrix of order @var{n}.  The
-## @tex
-## $i,\,j$
-## @end tex
-## @ifnottex
-## i, j
-## @end ifnottex
-## element of a Hilbert matrix is defined as
+## Return the Hilbert matrix of order @var{n}.  The @math{i,j} element
+## of a Hilbert matrix is defined as
 ## @tex
 ## $$
 ## H (i, j) = {1 \over (i + j - 1)}
@@ -38,7 +32,22 @@
 ## @end example
 ##
 ## @end ifnottex
-## @seealso{hankel, vander, sylvester_matrix, invhilb, toeplitz}
+##
+## Hilbert matrices are close to being singular which make them difficult to
+## invert with numerical routines.
+## Comparing the condition number of a random matrix 5x5 matrix with that of
+## a Hilbert matrix of order 5 reveals just how difficult the problem is.
+##
+## @example
+## @group
+## cond (rand (5))
+##     @result{} 14.392
+## cond (hilb (5))
+##     @result{} 4.7661e+05
+## @end group
+## @end example
+##
+## @seealso{invhilb}
 ## @end deftypefn
 
 ## Author: jwe