Given the truncated power series basis, e.g. the following functions: $1, x, x^2, ((x-\eta_0)^{+})^{2}, ((x-\eta_2)^+)^2, \dots ((x-\eta_{l+1})^+)^2$ there is a set of bspline-functions $s_1, \dots $ which can be shown to be linearly independent and span the same space as the above truncated power series.
My question: How can I determine the coefficients. That is, given a function from the truncated power series basis - e.g. $((x-1)^{+})^2$ -- how can I determine the coefficients $c_1, \dots$ such that $$((x-1)^{+})^2= \sum_i c_i s_i$$ holds. Note that I don't want to address this via computation because the resulting matrix expression is ill-conditioned. That is, I need an explicit formula for the coefficients.