概述了华罗庚先生仙逝前对经济优化理论的重要更新,该结果不幸沉睡了37年,直到2021年底才被唤醒;介绍了其后续进展,有一次修正、一次再更新和5项新发展:稳定性分析的新方法;产品(产业)等级(排序);预测与调整;经济结构的优化;重排序与大矩阵主特征值(及依大、小序的前6个特征值)的高效算法。难得的是,多种变换给出了完全相同的非稳定的时间和产品。早年关于华氏经济崩溃定理的证明基于马氏链的遍历定理,最近的全部结果基于马氏链的转移概率矩阵,也许可视为经济优化研究的新路子。这些成果已被应用于中国1个省级和5个国家级投入产出表,检验了理论的合理性和可靠性。
We summarize Loo-Keng Hua's important update on economic optimization theory before his immortal death, which unfortunately fell asleep for 37 years and was not awakened until the end of 2021. Next, we introduce its subsequent progress, including one revision, one re-update, and five new developments: a new method for stability analysis; product (industry) level (ranking); prediction and adjustment; optimization of economic structure; efficient algorithms for reordering and large matrix principal eigenvalues (as well as the top 6 eigenvalues in major and minor order). It is rare that multiple transformations provide exactly the same unstable time and product. In the early years, the proof of the Hua's economic collapse theorem was based on the ergodic theorem of the Markov chain, and the recent results are all based on the transition probability matrix of the Markov chain, which may be seen as a new approach to economic optimization research. These achievements have been applied to one provincial-level and five national level input-output tables in China, testing the rationality and reliability of the theory.
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