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## Stability of Levinson-Durbin method for Toeplitz system solutions ?

How stable is Levinson-Durbin method for solution of systems of linear equations ?

I mean if condition number of matrix is $k$, does intermidiate steps involve matrixes with higher condition number ? For example QR is easy to see preserve condition number so it is stable, but Cholesky for example increase condition number from $k$ to $k^2$, so Cholesky is less stable.

The question is related with possible fix-point implementation of this method and we need to understand how many bits should be given, for matrices of small size.

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 @Federico Thank you very much ! If matrices are positive definite, but may be not totally positive, if there any advice ? PS I do not have access to this paper :( If you can send me that would be great al.mylastname at gmail dot com – Alexander Chervov Aug 16 at 10:36 @Alexander The same paper shows some examples of PD matrices in which Levinson gives a much larger error than GKO and the conventional $O(n^3)$ Gaussian elimination methods. – Federico Poloni Aug 16 at 10:51 @Federico Thank you very much again !:) – Alexander Chervov Aug 17 at 6:21