Mercurial > octave-antonio

comparison scripts/special-matrix/hilb.m @ 20162:2645f9ef8c88 stable

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
doc: Update more docstrings to have one sentence summary as first line. Reviewed specfun, special-matrix, testfun, and time script directories. * scripts/specfun/expint.m, scripts/specfun/isprime.m, scripts/specfun/legendre.m, scripts/specfun/primes.m, scripts/specfun/reallog.m, scripts/specfun/realsqrt.m, scripts/special-matrix/gallery.m, scripts/special-matrix/hadamard.m, scripts/special-matrix/hankel.m, scripts/special-matrix/hilb.m, scripts/special-matrix/invhilb.m, scripts/special-matrix/magic.m, scripts/special-matrix/pascal.m, scripts/special-matrix/rosser.m, scripts/special-matrix/toeplitz.m, scripts/special-matrix/vander.m, scripts/special-matrix/wilkinson.m, scripts/testfun/assert.m, scripts/testfun/demo.m, scripts/testfun/example.m, scripts/testfun/fail.m, scripts/testfun/rundemos.m, scripts/testfun/runtests.m, scripts/testfun/speed.m, scripts/time/asctime.m, scripts/time/calendar.m, scripts/time/clock.m, scripts/time/ctime.m, scripts/time/datenum.m, scripts/time/datestr.m, scripts/time/datevec.m, scripts/time/etime.m, scripts/time/is_leap_year.m, scripts/time/now.m, scripts/time/weekday.m: Update more docstrings to have one sentence summary as first line.
author Rik <rik@octave.org>
date Sun, 03 May 2015 17:00:11 -0700
parents 4197fc428c7d
children
comparison
equal deleted inserted replaced
20160:03b9d17a2d95 20162:2645f9ef8c88
16 ## along with Octave; see the file COPYING. If not, see 16 ## along with Octave; see the file COPYING. If not, see
17 ## <http://www.gnu.org/licenses/>. 17 ## <http://www.gnu.org/licenses/>.
18 18
19 ## -*- texinfo -*- 19 ## -*- texinfo -*-
20 ## @deftypefn {Function File} {} hilb (@var{n}) 20 ## @deftypefn {Function File} {} hilb (@var{n})
21 ## Return the Hilbert matrix of order @var{n}. The @math{i,j} element 21 ## Return the Hilbert matrix of order @var{n}.
22 ## of a Hilbert matrix is defined as 22 ##
23 ## The @math{i,j} element of a Hilbert matrix is defined as
23 ## @tex 24 ## @tex
24 ## $$ 25 ## $$
25 ## H(i, j) = {1 \over (i + j - 1)} 26 ## H(i, j) = {1 \over (i + j - 1)}
26 ## $$ 27 ## $$
27 ## @end tex 28 ## @end tex
32 ## @end example 33 ## @end example
33 ## 34 ##
34 ## @end ifnottex 35 ## @end ifnottex
35 ## 36 ##
36 ## Hilbert matrices are close to being singular which make them difficult to 37 ## Hilbert matrices are close to being singular which make them difficult to
37 ## invert with numerical routines. 38 ## invert with numerical routines. Comparing the condition number of a random
38 ## Comparing the condition number of a random matrix 5x5 matrix with that of 39 ## matrix 5x5 matrix with that of a Hilbert matrix of order 5 reveals just how
39 ## a Hilbert matrix of order 5 reveals just how difficult the problem is. 40 ## difficult the problem is.
40 ## 41 ##
41 ## @example 42 ## @example
42 ## @group 43 ## @group
43 ## cond (rand (5)) 44 ## cond (rand (5))
44 ## @result{} 14.392 45 ## @result{} 14.392