Computing E-optimal polynomial regression designs

We consider the problem of computing E-optimal designs in heteroscedastic polynomial regression with not necessarily strictly positive efficiency function. Based on a relation between E- and c-optimal designs, a reasonable candidate for E-optimality is obtained from equioscillating weighted polynomials. Optimality of that candidate is easily checked, at least numerically. Moreover, nonoptimality of that design has some interesting consequences, e.g. on the support, which might be helpful to obtain the optimal design also in this case.For computing the candidate numerically we propose a procedure based on Remez's second algorithm. Convergence of that procedure is verified, extending a result of Studden and Tsay (1976). Numerical examples are presented for some efficiency functions.