Mercurial > hg > octave-max
changeset 5555:dbdba35033a6
[project @ 2005-11-30 16:12:04 by jwe]
| author | jwe |
|---|---|
| date | Wed, 30 Nov 2005 16:12:04 +0000 |
| parents | 3f1a39aa2012 |
| children | dc24a787b96b |
| files | scripts/ChangeLog scripts/linear-algebra/krylov.m src/ChangeLog src/DLD-FUNCTIONS/schur.cc |
| diffstat | 4 files changed, 37 insertions(+), 21 deletions(-) [+] |
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--- a/scripts/ChangeLog +++ b/scripts/ChangeLog @@ -1,3 +1,8 @@ +2005-11-30 John W. Eaton <jwe@octave.org> + + * linear-algebra/krylov.m: Format doc string. + From Jorge Barros de Abreu <ficmatin01@solar.com.br>. + 2005-11-23 William Poetra Yoga Hadisoeseno <williampoetra@yahoo.com> * general/blkdiag.m: Import from octave-forge.
--- a/scripts/linear-algebra/krylov.m +++ b/scripts/linear-algebra/krylov.m @@ -18,28 +18,34 @@ ## 02110-1301 USA. ## -*- texinfo -*- -## @deftypefn {Function File} {[@var{u}, @var{h}, @var{nu}] =} krylov (@var{a}, @var{v}, @var{k}, @var{eps1}, @var{pflg}); -## construct orthogonal basis U of block Krylov subspace; -## [v a*v a^2*v ... a^(k+1)*v]; -## method used: householder reflections to guard against loss of -## orthogonality -## eps1: threshhold for 0 (default: 1e-12) -## pflg: flag to use row pivoting (improves numerical behavior) -## 0 [default]: no pivoting; prints a warning message if trivial -## null space is corrupted -## 1 : pivoting performed +## @deftypefn {Function File} {[@var{u}, @var{h}, @var{nu}] =} krylov (@var{a}, @var{v}, @var{k}, @var{eps1}, @var{pflg}) +## Construct an orthogonal basis @var{u} of block Krylov subspace +## +## @example +## [v a*v a^2*v ... a^(k+1)*v] +## @end example +## +## @noindent +## Using Householder reflections to guard against loss of orthogonality. ## -## outputs: -## u: orthogonal basis of block krylov subspace -## h: Hessenberg matrix; if v is a vector then a u = u h -## otherwise h is meaningless -## nu: dimension of span of krylov subspace (based on eps1) -## if b is a vector and k > m-1, krylov returns h = the Hessenberg -## decompostion of a. +## If @var{v} is a vector, then @var{h} contains the Hessenberg matrix +## such that @code{a*u == u*h}. Otherwise, @var{h} is meaningless. +## +## The value of @var{nu} is the dimension of the span of the krylov +## subspace (based on @var{eps1}). +## +## If @var{b} is a vector and @var{k} is greater than @var{m-1}, then +## @var{h} contains the Hessenberg decompostion of @var{a}. +## +## The optional parameter @var{eps1} is the threshold for zero. The +## default value is 1e-12. +## +## If the optional parameter @var{pflg} is nonzero, row pivoting is used +## to improve numerical behavior. The default value is 0. ## ## Reference: Hodel and Misra, "Partial Pivoting in the Computation of -## Krylov Subspaces", to be submitted to Linear Algebra and its -## Applications +## Krylov Subspaces", to be submitted to Linear Algebra and its +## Applications ## @end deftypefn ## Author: A. Scottedward Hodel <a.s.hodel@eng.auburn.edu>