Description:
<p>In this paper we investigate (d+1)-point D-optimal designs for dth degree polynomial regression with weight function ω(x) ≥ 0 on the interval [a,b]. We propose an algebraic approach and provide a numerical method for the construction of optimal designs. Thus if ω′(x)/ω(x) is a rational function and the information of whether the optimal support contains the boundary points a and b is available, the problem of constructing (d + 1)-point D-optimal designs can be transformed into a differential equation problem. One is led to a matrix that includes a finite number of auxiliary unknown constants, and the differentiation can be solved from a system of polynomial equations in those constants. Moreover, the (d + 1)-point D-optimal interior support points are the zeros of a polynomial whose coefficients can be computed from a linear system.</p>