In order to clarify the coordinated development status between the digital economy and the ecological environment in the context of rapid development of the digital economy and frequent ecological environment problems, we constructed an evaluation system using data related to the digital economy and the ecological environment in China from 2011 to 2019. And the level of coordinated development is calculated with the help of entropy method and the Coupling Coordinated Development (CCD) model. Further, we analyzed the spatial and temporal evolutionary trends of their coordinated development levels with the kernel density analysis and the Dagum Gini coefficient decomposition. The results of the entropy method and CCD show that both the level of digital economy, the level of ecological environment and the level of coupling coordination between the two have increased. And the level of coordinated development shows regional heterogeneity, with the highest in the eastern region, followed by the central region, and the lowest in the western region. The results of the kernel density analysis show that there is heterogeneity in the development process of CCD scores over time across regions. The results of the Dagum Gini coefficient decomposition show that the overall inter-regional differences, as well as intra-regional differences, are fluctuating and decreasing. And the overall imbalance mainly comes from the differences in development levels between regions. The analysis of the above methods provides a basis for understanding the spatial and temporal evolution characteristics of the coordinated development of China’s digital economy and ecological environment. And it also provides relevant policy recommendations for promoting coordinated and sustainable development among regions.

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In this paper, we study the D- and A-optimal assignment problems for regression models with experimental cost constraints. To solve these two problems, we propose two multiplicative algorithms for obtaining optimal designs and establishing extended D-optimal (ED-optimal) and A-optimal (EA-optimal) criteria. In addition, we give proof of the convergence of the ED-optimal algorithm and draw conjectures about some properties of the EA-optimal algorithm. Compared with the classical D- and A-optimal algorithms, the ED- and EA-optimal algorithms consider not only the accuracy of parameter estimation, but also the experimental cost constraint. The proposed methods work well in the digital example.

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