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comparison scripts/linear-algebra/krylov.m @ 20160:03b9d17a2d95 stable

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doc: Update more docstrings to have one sentence summary as first line. Reviewed io, java, linear-algebra, prefs, and set script directories. * scripts/io/beep.m, scripts/io/dlmwrite.m, scripts/io/importdata.m, scripts/io/strread.m, scripts/io/textread.m, scripts/java/javaArray.m, scripts/java/java_get.m, scripts/java/java_set.m, scripts/java/javaaddpath.m, scripts/java/javachk.m, scripts/java/javaclasspath.m, scripts/java/javamem.m, scripts/java/javarmpath.m, scripts/linear-algebra/bandwidth.m, scripts/linear-algebra/commutation_matrix.m, scripts/linear-algebra/cond.m, scripts/linear-algebra/condest.m, scripts/linear-algebra/cross.m, scripts/linear-algebra/duplication_matrix.m, scripts/linear-algebra/expm.m, scripts/linear-algebra/housh.m, scripts/linear-algebra/isdefinite.m, scripts/linear-algebra/ishermitian.m, scripts/linear-algebra/issymmetric.m, scripts/linear-algebra/istril.m, scripts/linear-algebra/istriu.m, scripts/linear-algebra/krylov.m, scripts/linear-algebra/logm.m, scripts/linear-algebra/normest.m, scripts/linear-algebra/null.m, scripts/linear-algebra/onenormest.m, scripts/linear-algebra/orth.m, scripts/linear-algebra/qzhess.m, scripts/linear-algebra/rank.m, scripts/linear-algebra/rref.m, scripts/linear-algebra/vech.m, scripts/path/matlabroot.m, scripts/prefs/addpref.m, scripts/prefs/getpref.m, scripts/prefs/ispref.m, scripts/prefs/rmpref.m, scripts/prefs/setpref.m, scripts/set/powerset.m, scripts/set/setdiff.m: Update more docstrings to have one sentence summary as first line.
author Rik <rik@octave.org>
date Sun, 03 May 2015 15:36:23 -0700
parents 4197fc428c7d
children
comparison
equal deleted inserted replaced
20159:597991b19e40 20160:03b9d17a2d95
23 ## @example 23 ## @example
24 ## [v a*v a^2*v @dots{} a^(k+1)*v] 24 ## [v a*v a^2*v @dots{} a^(k+1)*v]
25 ## @end example 25 ## @end example
26 ## 26 ##
27 ## @noindent 27 ## @noindent
28 ## Using Householder reflections to guard against loss of orthogonality. 28 ## using Householder reflections to guard against loss of orthogonality.
29 ## 29 ##
30 ## If @var{V} is a vector, then @var{h} contains the Hessenberg matrix 30 ## If @var{V} is a vector, then @var{h} contains the Hessenberg matrix
31 ## such that @nospell{@tcode{a*u == u*h+rk*ek'}}, in which @code{rk = 31 ## such that @nospell{@tcode{a*u == u*h+rk*ek'}}, in which
32 ## a*u(:,k)-u*h(:,k)}, and @nospell{@tcode{ek'}} is the vector 32 ## @code{rk = a*u(:,k)-u*h(:,k)}, and @nospell{@tcode{ek'}} is the vector
33 ## @code{[0, 0, @dots{}, 1]} of length @code{k}. Otherwise, @var{h} is 33 ## @code{[0, 0, @dots{}, 1]} of length @code{k}. Otherwise, @var{h} is
34 ## meaningless. 34 ## meaningless.
35 ## 35 ##
36 ## If @var{V} is a vector and @var{k} is greater than 36 ## If @var{V} is a vector and @var{k} is greater than @code{length (A) - 1},
37 ## @code{length (A) - 1}, then @var{h} contains the Hessenberg matrix such 37 ## then @var{h} contains the Hessenberg matrix such that @code{a*u == u*h}.
38 ## that @code{a*u == u*h}. 38 ##
39 ## 39 ## The value of @var{nu} is the dimension of the span of the Krylov subspace
40 ## The value of @var{nu} is the dimension of the span of the Krylov 40 ## (based on @var{eps1}).
41 ## subspace (based on @var{eps1}). 41 ##
42 ## 42 ## If @var{b} is a vector and @var{k} is greater than @var{m-1}, then @var{h}
43 ## If @var{b} is a vector and @var{k} is greater than @var{m-1}, then 43 ## contains the Hessenberg decomposition of @var{A}.
44 ## @var{h} contains the Hessenberg decomposition of @var{A}. 44 ##
45 ## 45 ## The optional parameter @var{eps1} is the threshold for zero. The default
46 ## The optional parameter @var{eps1} is the threshold for zero. The 46 ## value is 1e-12.
47 ## default value is 1e-12. 47 ##
48 ## 48 ## If the optional parameter @var{pflg} is nonzero, row pivoting is used to
49 ## If the optional parameter @var{pflg} is nonzero, row pivoting is used 49 ## improve numerical behavior. The default value is 0.
50 ## to improve numerical behavior. The default value is 0.
51 ## 50 ##
52 ## Reference: @nospell{A. Hodel, P. Misra}, @cite{Partial Pivoting in the 51 ## Reference: @nospell{A. Hodel, P. Misra}, @cite{Partial Pivoting in the
53 ## Computation of Krylov Subspaces of Large Sparse Systems}, Proceedings of 52 ## Computation of Krylov Subspaces of Large Sparse Systems}, Proceedings of
54 ## the 42nd IEEE Conference on Decision and Control, December 2003. 53 ## the 42nd IEEE Conference on Decision and Control, December 2003.
55 ## @end deftypefn 54 ## @end deftypefn