Past exam of the options II course of the University of Oxford / 2011 / P / P3 / a

A polynomial least-squares approximation $p_n\in {\Pi }_n$ minimizes the weighted residual norm:Equivalently it minimizes ${\int }_{-1}^1{x}^2(u(x)-q(x){)}^{2}dx$. This is a best approximation within a finite-dimensional polynomial space, without an interpolation requirement.