[Pd] Toeplitz solver libraries? Is there a new fast routine anywhere?

Mathieu Bouchard matju at artengine.ca
Fri Feb 17 22:11:17 CET 2006

On Thu, 16 Feb 2006, Charles Henry wrote:

>   I was wondering if anyone knows of a (preferably free) library for
> solving a toeplitz matrix equation

Apparently, if your Toeplitz matrices are circulant, then there's an easy
isomorphism with pointwise multiplication, using FFT, e.g. [fft~], because
a circulant matrix is like a cyclic convolution product, which can be seen
as a polynomial product on the space R[x]/(x^n-1).

If they are not circulant, then I guess you can fake it by considering
them each as the sum of a circulant matrix and a simpler matrix. The
latter is actually a triangular Toeplitz minus its transpose. I think 
that it'd be rather simple to FFTize that for general Toeplitzes of 
size 3x3, 7x7, 15x15, etc., but I haven't tried.

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| Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
| Freelance Digital Arts Engineer, Montréal QC Canada

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