Abstract: In this paper we investigate-point
-optimal designs for
th degree polynomial regression with weight function
on the interval
. We propose an algebraic approach and provide a numerical method for the construction of optimal designs. Thus if
is a rational function and the information of whether the optimal support contains the boundary points
and
is available, the problem of constructing
-point
-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
-point
-optimal interior support points are the zeros of a polynomial whose coefficients can be computed from a linear system.
Key words and phrases: Approximate D-optimal design, differential equation, matrix, minimally-supported, rational function, weighted polynomial regression.