tricky matrix problem

[Jewel Bright <jwlbright@yahoo.com>]

Dear Friends:

The question I am about to ask is not exactly an S-PLUS or even statistical one, so those of you who stick with rigorous rules of using this discussion forum please disregard this message. However, those of you who have a strong mathematical background may find the problem curious. It is equally possible that the problem is a kind of trivial, but unfortunately it is above my level of education.

 

I have a 3-dimensional array which I denote as K(i|a,b) with all the i, a, and b in 1:n. I need to solve the system of nonlinear algebraic equations:

 

(x[i])^2=Sum(over a) Sum(over b){K[i|a,b)*x[a]*x[b]

 

I have not have any difficulties to solve the problem numerically using nlminb, but I have no idea whether or not this solution is unique, and whether or not there is some theory for this kind of equations.

 

Any thoughts or references are highly appreciated

 

Thanks

Jewel

 

 

 

 

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