Re: [eigen] Problem inverting a Matrix4f with Eigen 2.0.0

[Aron Ahmadia <aja2111@xxxxxxxxxxxx>]

I admit that pointing to LAPACK was a bad example (I am least familiar
with that package of those mentioned), however, MATLAB and NumPy are
far more common these days as computational interfaces than LAPACK
(even if they are built on top of its routines).

A

On Sat, Jul 17, 2010 at 6:55 PM, Aron Ahmadia <aja2111@xxxxxxxxxxxx> wrote:
> Hi Benoit,
>
> Sorry, I meant the inverse in this sense, this is something that
> arises when solving the two problems:
>
> Ab = x
> Ax = b
>
> Where I leave the unknown as x, and the fixed as b.  Both problems can
> be bound by a condition number that depends on the perturbations of x
>
> \kappa = ||A||*||b||/||x||     <= ||A||*||A^-1|| (forward)
> \kappa = ||A^-1||*||b||/||x|| <= ||A||*||A^-1|| (backward)
>
> The term ||A||*||A^-1||, since it arises in both forward and backward
> problems, is called the condition number of A.  This is pretty solidly
> in the literature, and you wouldn't confuse anybody if you had a
> general "calculate the condition number of a matrix" function and more
> specialized ones for calculating the condition numbers of other
> specific operations.
>
> A
>