Abstract: The paper established an evaluation index system of the city competitiveness of Zhongyuan Urban Agglomeration, and used principal component analysis to evaluate the city competitiveness in 1988, 1992, 1998 and 2006, respectively. Moreover, the paper studied time evolvement of the city competitiveness. The index system includes basic competitiveness, economic competitiveness, science and technology competitiveness, opening competitiveness, government function, environment competitiveness, and 15 element layer indexes, as well as 40 basic variable layer indexes. In actual problems, it is common that several maximal principal components are selected. The paper used calculated results of the city competitiveness, space expression method and space interpolation method to research space evolvement of the city competitiveness of Zhongyuan Urban Agglomeration. According to comprehensive scores, the cities are divided into four grades, >1.5, 1.5 to -0.5, -0.5 to -2 and <-2. Cities in different grades are expressed in the map of Zhengzhou Urban Agglomeration with different colors, and the evolution situation of spatial differentiation of the city competitiveness is expressed through different time sections. The paper selects brief and exact spatial interpolation method—IDM (Inverse Distance Weighted) to research the evaluation situation of spatial patulous of the city competitiveness. Numerical value of interpolation points that are calculated will be automatically created in the city competitiveness map, and the effect maps are formed about the city competitiveness.According to the analysis result, the basic points of view are obtained as follows: (1) Principal component and comprehensive scores of the city competitiveness of nine cities for four time sections were calculated, and the city competitiveness was evaluated and sorted. (2) According to the evaluation result, the rules and features of general evolution, principal component evaluation, influencing factors in evolution of the city competitiveness of Zhongyuan Urban Agglomeration, were revealed. (3) The evolution laws and features of spatial differentiation and spatial expansion of the city competitiveness of Zhongyuan Urban Agglomeration were revealed through analysis of grade maps and effect maps in different stages.

Key words: city competitiveness, principal component analysis, space expression, spatial interpolation, Zhongyuan Urban Agglomeration