Levinson-Durbin for Least Squares

Cagdas Ozgenc

unread,

Apr 23, 2010, 5:49:20 AM4/23/10

to

Hello,

In DSP related articles Levinson-Durbin method for finding Wiener-Hopf
solution is taken for granted whereas in Least Squares related
articles seem to ignore this method. I read that in order to use
Levinson-Durbin correlation matrix for inputs should be Toeplitz.

Under what kind of assumptions I end-up with a Toeplitz correlation
matrix? How is Wiener-Hopf different from Least Squares regression?

Thanks

Gordon Sande

unread,

Apr 23, 2010, 8:43:31 AM4/23/10

to

In one situation (DSP) the discussion is about the autocorrelation function.
In the other situation the discussion is about the correlation matrix.

Have you asked how to represent an autocorrelation as a matrix? What are
the conditons for a Toeplitz matrix? Have you answered your own question
by answering the previoous two questions?

Cagdas Ozgenc

unread,

Apr 23, 2010, 9:36:34 AM4/23/10

to

On Apr 23, 4:43 pm, Gordon Sande <Gordon.Sa...@EastLink.ca> wrote:

Not really. Basically my question is is it always possible to use
Levinson-Durbin in linear least square regression problems?

Gordon Sande

unread,

Apr 23, 2010, 9:56:14 AM4/23/10

to

When the correlation matrix is not Topelitz why would you think that a
method that assumes a Toeplitz matrix would work?

By the way, many of the Toeplitz specific methods are prone to numerical
stability problems. It is the price of the lower operation counts. The
computation cost is rarely an issue with current computers.

Cagdas Ozgenc

unread,

Apr 23, 2010, 10:01:52 AM4/23/10

to

On Apr 23, 5:56 pm, Gordon Sande <Gordon.Sa...@EastLink.ca> wrote:

> computation cost is rarely an issue with current computers.- Hide quoted text -
>
> - Show quoted text -

That's why getting back to the previous question: Under what
conditions my correlation matrix will be a Toeplitz matrix, isn't it
always the case?

Computation cost is still an issue. Inverting a 1000x1000 matrix takes
some time even in today's computers.

Gordon Sande

unread,

Apr 23, 2010, 11:11:50 AM4/23/10

to

No!

When do you have a correlation matrix and when do you have an autocorrelation
function? If you give the glib answer of "you always have a corelation matrix"
then the question will be refined to when is a correlation matrix Toeplitz?
Or when is a symmetric positive definte matrix (like a correlation matrix) also
Toeplitz? Or is least squares restricted to being applied to time series?

> Computation cost is still an issue. Inverting a 1000x1000 matrix takes
> some time even in today's computers.

Only if you have a very slow computer or are intending to do it very often.
Or if you think a any time greater than zero is an issue for the purpose of
putting an argument. That is why the adjective rarely was used.

Cagdas Ozgenc

unread,

Apr 24, 2010, 2:14:56 AM4/24/10

to

> putting an argument. That is why the adjective rarely was used.- Alıntıyı gizle -
>
> - Alıntıyı göster -

Ok, ok, I get it. If I prepare a correlation matrix (or even a
covariance matrix) from the lagged values of a second order stationary
process I will end up with a Toeplitz correlation matrix. Otherwise it
will be only positive semi definite.