In a recent paper Pukelsheim and Studden determined the $E$-optimal design for the polynomial regression model on the interval $\lbrack - 1, 1\rbrack$ where the variances of different observations are assumed to be constant. In this note we show that these results can be generalized for polynomial regression models with non constant variances proportional to specific functions.
"A Note on $E$-Optimal Designs for Weighted Polynomial Regression." Ann. Statist. 21 (2) 767 - 771, June, 1993. https://doi.org/10.1214/aos/1176349150