[Insight-users] polynomial fitting for fcMRI processing

[J.S.Wijnhout at lumc.nl]

> You are right. I was speaking about non-linear least squares 
> which has little to do with polynomial fitting (no matter if 
> the polynomial itself is or is not linear - different notion 
> of linearity).

Ah, ok.

> But still isn't it possible that symbolic solution could be 
> numerically unstable?

That is indeed possible. In that case you have to solve the matrix
equation
numerically (still easier to do than full Levenberg-Marquardt). I have
no
clue when such a situation occurs in practice, but it is easy to detect
beforehand:
the determinant of the matrix becomes close to zero. You can always
check for that
and use Levenberg-Marquardt (for example) if the determinant is close to
zero.

> "This matrix equation can be solved numerically, or can be 
> inverted directly if it is well formed, to yield the solution 
> vector" [from the link you posted]

best,
Jeroen