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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