Re: [eigen] LeastSquares, Pseudo Inverse & Geometry

[Thomas Capricelli <orzel@xxxxxxxxxxxxxxx>]

On Monday 25 January 2010 09:51:24 Manuel Yguel wrote:
> Hello, I think that this is because the covariance matrix is symmetric
> semi-definite positive, therefore, eigenvalues and singular value
> decomposition look the same

MM. right, the covariance matrix is symmetric, hence we can use some eigen* computation.

But why is it so here while it's not in the general case ? Am I right saying that this only applies when computing a linear least-square to fit (hyper)planes ? so that this is a special case(hyperplanes) inside a special case (linear least squares).

I use both linear/non linear least squares, but never on hyperplanes :-)

> By the way I just wanted to know if this knowledge makes the
> computation faster, i.e. is the eigenvalues/eigenvectors computation
> faster than the SVD in this case.

I wonder too, please share your results if you do some comparisons.

++
-- 
Thomas Capricelli <orzel@xxxxxxxxxxxxxxx>
http://www.freehackers.org/thomas