chebychev interpolation and Gaussian quadrature schemes

Hi guys, I have a problem and I would like some help if possible. I am busy studying the mutual influences of the price of one good on another. In order to do so, we came up with the following model Xi = αi – aPi + bPj (1) Xj = αj + bPi – cP j (2) I would like to use the Chebychev algorithm interpolation and Gaussian quadrature schemes to approximate the parameters αi, αj, a, b and c. I also know that this is linear system of equations :

[John D'Errico]

Great. So you have told us very vaguely what you would like to do. Only you know what you intend to happen by using those algorithms, as they make no sense in context of what you have said. Just throwing jargon around will not get you an answer. In fact, if you are only able to explain what you want to do so poorly, then odds are that you won't find those methods of any use at all for what you eventually do.