comparison scripts/linear-algebra/expm.m @ 10791:3140cb7a05a1

Add spellchecker scripts for Octave and run spellcheck of documentation interpreter/doccheck: New directory for spelling/grammar scripts. interpreter/doccheck/README: Instructions for using scripts. interpreter/doccheck/spellcheck: Script to spellcheck a Texinfo file. interpreter/doccheck/aspell.conf: GNU Aspell configuration file for Octave documentation. interpreter/doccheck/aspell-octave.en.pws: Private Aspell dictionary. interpreter/doccheck/add_to_aspell_dict: Script to add new Octave-specific words to private Aspell dictionary. interpreter/octave.texi: New @nospell macro which forces Aspell to ignore the word marked by the macro. interpreter/mk_doc_cache.m: Skip new @nospell macro when building doc_cache.
author Rik <octave@nomad.inbox5.com>
date Sat, 17 Jul 2010 19:53:01 -0700
parents d1978e7364ad
children 1646bd8e3735
comparison
equal deleted inserted replaced
10790:01f1643dfbb1 10791:3140cb7a05a1
33 ## 33 ##
34 ## @end ifnottex 34 ## @end ifnottex
35 ## The Taylor series is @emph{not} the way to compute the matrix 35 ## The Taylor series is @emph{not} the way to compute the matrix
36 ## exponential; see Moler and Van Loan, @cite{Nineteen Dubious Ways to 36 ## exponential; see Moler and Van Loan, @cite{Nineteen Dubious Ways to
37 ## Compute the Exponential of a Matrix}, SIAM Review, 1978. This routine 37 ## Compute the Exponential of a Matrix}, SIAM Review, 1978. This routine
38 ## uses Ward's diagonal 38 ## uses Ward's diagonal Pad@'e approximation method with three step
39 ## @tex 39 ## preconditioning (SIAM Journal on Numerical Analysis, 1977). Diagonal
40 ## Pad\'e 40 ## Pad@'e approximations are rational polynomials of matrices
41 ## @end tex
42 ## @ifnottex
43 ## Pade'
44 ## @end ifnottex
45 ## approximation method with three step preconditioning (SIAM Journal on
46 ## Numerical Analysis, 1977). Diagonal
47 ## @tex
48 ## Pad\'e
49 ## @end tex
50 ## @ifnottex
51 ## Pade'
52 ## @end ifnottex
53 ## approximations are rational polynomials of matrices
54 ## @tex 41 ## @tex
55 ## $D_q(a)^{-1}N_q(a)$ 42 ## $D_q(a)^{-1}N_q(a)$
56 ## @end tex 43 ## @end tex
57 ## @ifnottex 44 ## @ifnottex
58 ## 45 ##
62 ## D (a) N (a) 49 ## D (a) N (a)
63 ## @end group 50 ## @end group
64 ## @end example 51 ## @end example
65 ## 52 ##
66 ## @end ifnottex 53 ## @end ifnottex
67 ## whose Taylor series matches the first 54 ## whose Taylor series matches the first
68 ## @tex 55 ## @tex
69 ## $2 q + 1 $ 56 ## $2 q + 1 $
70 ## @end tex 57 ## @end tex
71 ## @ifnottex 58 ## @ifnottex
72 ## @code{2q+1} 59 ## @code{2q+1}
73 ## @end ifnottex 60 ## @end ifnottex
74 ## terms of the Taylor series above; direct evaluation of the Taylor series 61 ## terms of the Taylor series above; direct evaluation of the Taylor series
75 ## (with the same preconditioning steps) may be desirable in lieu of the 62 ## (with the same preconditioning steps) may be desirable in lieu of the
76 ## @tex 63 ## Pad@'e approximation when
77 ## Pad\'e
78 ## @end tex
79 ## @ifnottex
80 ## Pade'
81 ## @end ifnottex
82 ## approximation when
83 ## @tex 64 ## @tex
84 ## $D_q(a)$ 65 ## $D_q(a)$
85 ## @end tex 66 ## @end tex
86 ## @ifnottex 67 ## @ifnottex
87 ## @code{Dq(a)} 68 ## @code{Dq(a)}