We are all familiar with the system of linear equations:

a11 x1 + a12 x2 + ... + a1n xn = b1

a21 x1 + a22 x2 + ... + a2n xn = b2...

an1 x1 + an2 x2 + ... + ann xn = bn

Has anyone seen an application for the variant of the above such that:

a11 x1^2 + a12 x2 + ... + a1n xn = b1

a21 x1 + a22 x2^2 + ... + a2n xn = b2

...

an1 x1 + an2 x2 + ... + ann xn^2 = bn

In other words, where the i'th diagonal element has the square (or even any other power that is not equal to one) of xi instead just xi.

Thanks!

Namir

*Edited: 2 June 2012, 5:42 p.m. *