在這一篇論文裡面，針對多項式回歸模型的加權D最適設計來探討。
假設w'(x)/w(x)是有理函數，而且已經知道端點是否為設計點， 則建構D最適設計的問題可以換成是微分方程的問題。這裡我們只考慮方程式未知數為一個或零個的情況，近而去刻畫所對應的權重。此外，在當未知數為一個的時候，也可以把原先的微分方成問題利用特徵值問題去解決。
在本篇的後面提供了數值的結果，他們說明了最適設計與順序特徵值的有趣關係。

In this paper we investigate (d + 1)-point D-optimal designs for d-th degree polynomial
regression with weight function w(x) > 0 on the interval [a, b]. Suppose that w'(x)/w(x) is a rational function and the information of whether the optimal support
contains the boundary points a and b is available. Then the problem of constructing
(d + 1)-point D-optimal designs can be transformed into a differential equation
problem leading us to a certain matrix with k auxiliary unknown constants. We characterize the weight functions corresponding to the cases when k= 0 and k= 1.
Then, we can solve (d + 1)-point D-optimal designs directly from differential equation
(k = 0) or via eigenvalue problems (k = 1). The numerical results show us an interesting relationship between optimal designs and ordered eigenvalues.

Introduction
Premilinaries
Characterization of weight functions
Examples
Conclusion
Appendix
Reference

Antille, G., Dette, H. and Weinberg, A. (2003). A note on optimal designs in weighted
polynomial regression for the classical e_ciency functions. J. Statist. Plann. Inference
113, 285-292.
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Atkinson, A.C. and Donev, A.N. (1992). Optimum Experimental Designs. Oxford University
Press, New York.
Chang, F.-C. (2005).