[Insight-developers] Numerical methods: an example of places that need improvement.

[Wes Turner]

Most of the iterative libraries also provide preconditioning strategies
which can help when the condition number goes up.  Yousef Saad and the Petsc
guys both have libraries of iterative solvers with preconditioning ... I am
certain there are more.  Note that even direct methods will fail if the
condition number gets high enough ...

- Wes

On Fri, Nov 5, 2010 at 8:39 AM, Jim Miller <millerjv at gmail.com> wrote:

> I guess for certain problem sizes where the problem is well conditioned it
> shouldn't matter too much. But I imagine in the bspline code this is a hefty
> system of equations.
>
>
>
> On Nov 3, 2010, at 3:38 PM, Luis Ibanez <luis.ibanez at kitware.com> wrote:
>
> From our tcon on image registration.
>
>
> The following code:
>
>   vnl_matrix<double> B =
>     vnl_matrix_inverse<double>( N_matrix.transpose() * N_matrix) *
> N_matrix.transpose() * data_matrix;
>
> is from
>
> Insight/Code/Common/
> itkNonUniformBSpline.txx
> (line 313).
>
> <http://public.kitware.com/cgi-bin/viewcvs.cgi/Code/Common/itkNonUniformBSpline.txx?revision=1.9&root=Insight&view=markup>
> http://public.kitware.com/cgi-bin/viewcvs.cgi/Code/Common/itkNonUniformBSpline.txx?revision=1.9&root=Insight&view=markup
>
>
> It is trying to solve the linear system
>
>              X  = N * B
>
> by doing:
>
>         B = ( N' * N )^-1  *  N'  * X
>
>
> instead of invoking one of the linear solvers
> that we are carrying in ITK via VXL.
>
>
> ----
>
>
>    Luis
>
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-- 
Wesley D. Turner, Ph.D.
Kitware, Inc.
Technical Leader
28 Corporate Drive
Clifton Park, NY 12065-8662
Phone: 518-881-4920
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