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Subsections
We have a set of independent vectors
. We want to convert it into a set of orthonormal vectors
by the Gram-Schmidt process.
The scalar product between vectors
and
will be noted
- Initialization
,
- Orthogonalisation
![$\displaystyle \tilde{b_k}= a_k -
\sum_{j=1}^{k} <a_k, b_j> b_j$](img1359.png) |
(13.15) |
We will take
and transform
it into
by removing from
the component of
parallel to all the previously determined
.
- Normalisation
![$\displaystyle b_k= \frac{ \tilde{b_k} }{ \Vert
\tilde{b_k} \Vert }$](img1363.png) |
(13.16) |
- Loop increment
. If
go to step 2.
Algorithm 2.
- Initialization k=1;
- Normalisation
![$\displaystyle b_k=\frac{ a_k}{ \Vert a_k \Vert}$](img1365.png) |
(13.17) |
- Orthogonalisation for
to
do:
![$\displaystyle a_j= a_j
- <a_j, b_k> b_k \quad j=k+1, \ldots, n$](img1367.png) |
(13.18) |
We will take the
which are left and remove from all of them the component parallel
to the current vector
.
- Loop increment
. If
go to step 2.
Next: Notions of constrained optimization
Up: Annexes
Previous: Line-Search addenda.
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Frank Vanden Berghen
2004-04-19