Abstract: Ternary interval number includes the total GDP amount in a certain period and its change range. Comprehensive information is more conducive to management decision-making. Affected by regional characteristics and national macro-control, the development trend of GDP in various regions of China in the past 15 years has been different. Some central regions grew rapidly in the early stage and fell back in the later stage, showing a saturated growth trend. Some coastal economically developed areas showed exponential growth. While some regions show an unstable upward and downward fluctuation trend. In order to predict the development trend of different GDPs, a matrix model based on exponential and polynomial regression, which can directly model the ternary interval number, is proposed in this paper. In order to eliminate the random fluctuation of data, the original ternary interval number sequence is accumulated based on the data preprocessing method in the grey model, which makes the general non-negative sequence show quasi-exponential growth so that it can be applied to the exponential-polynomial matrix model. The particle swarm optimization algorithm and the least square method are combined to estimate the parameters of the new model. The new model, quadratic polynomial, GM (1, 1), and exponential function are used to predict the GDP of 31 regions in China from 2005 to 2020. The results show that the effect of the new model is better than other models in predicting GDP for 20 regions. 

Key words: Exponential and Polynomial Regression, Ternary Interval Number, Accumulation Generating Operator, Particle Swarm Optimization Algorithm