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I have a function that looks like this:

y = a1*x1*a2*x2*a3*x3....an*xn

All the parameters of the polynom (a1, a2, a3, ... an) are unknown.

Is there a way to find them using a small-medium (less than n) set of examples where each example is a set of xs (x1, x2, x3, ... xn) and y.

I know that there is no way to find these values perfectly but accurate enough answer (each new example raises the accuracy) will be ok.

Is it possible to do the same thing with n or more examples perfectly? and what about infinite number of examples.

edit:

BTW, why doesn't this latex work:

[tex] y = x_1a_1x_2a_2x_3a_3...x_na_n [/tex]

edit2:

as well as this:

[tex]y=x[/tex]

[tex]3*6[/tex]

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# Parameters of the polynom

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