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From a paper I got a matrix like this which I use to solve the over-determined system [itex]\mathbf{z} = \mathbf{U} \mathbf{a}[/itex]:

[tex]

\mathbf{U} = \left[\begin{matrix}

x(3) & x(3)^2 & x(3)^3 & x(2) & x(2)^2 & x(2)^3 & x(1) & x(1)^2 & x(1)^3\\

x(4) & x(4)^2 & x(4)^3 & x(3) & x(3)^2 & x(3)^3 & x(2) & x(2)^2 & x(2)^3\\

x(5) & x(5)^2 & x(5)^3 & x(4) & x(4)^2 & x(4)^3 & x(3) & x(3)^2 & x(3)^3\\

x(6) & x(6)^2 & x(6)^3 & x(5) & x(5)^2 & x(5)^3 & x(4) & x(4)^2 & x(4)^3\\

\end{matrix}\right]

[/tex]

However, in my experiments I found that this matrix is very unstable and has high condition numbers. No matter which "signal" x I plug into, even if the x are drawn from a Gaussian distribution.

Can anyone tell me why this matrix is so unstable or if I am doing something wrong?

The crazy thing is that the paper suggests the algorithm works without any problems (using the same parameter set) but I just can't reproduce this ...

Thanks,

div

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# Why is this matrix bad conditioned?

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