Re: matrix functions

[Bård Skaflestad]

On Tue, 2010-12-21 at 10:34 +0100, CdeMills wrote:
> Hello,
> 
> one of the basis of linear algebra is the decomposition of a square matrix
> into eigenvalues and eigenvectors, such that
> [V, D] = eig(A)
> A = V*D*inv(V)

[leads to]

> 
> f(A) = V[f(D)]inv(V)

I was about to suggest you use the 'funm' function, but now I see that
'funm' is only available (by default) in That Other Software.  On the
other hand, the 'linear-algebra' add-on package from OctaveForge does
contain a 'funm' implementation.  I haven't used it (or any other such
packages for that matter), but you may want to start from there.

Do note, however, that the eigenvalue expansion might not have the best
cost/benefit ratio.  Other implementations I've seen are based on the
Schur decomposition of the matrix rather than the eigenvalue
decomposition.  Also, if you can bound the norm(A) you may want to look
into Padé approximations.


Regards,
-- 
Bård Skaflestad <address@hidden>
SINTEF ICT, Applied Mathematics