Using the Cubic Spline Interpolation Method to Approximate Some Real Data

In engineering and science problems, the data being considered are of-ten known in the form of sets of discrete points, not as a continuous function. In applications, the values of the discrete data at specific points may be required to estimate. To solve these problems, a common mathematical ap-proach is to use the interpolation method. In this paper, we use the cubic natural spline interpolation method to build approxi-mate functions for some real data in Vietnam such as data on rice out-put and rice area of cultivation, data on expenditure and income per capita. The data used in this paper are extracted from the General Statis-tics Office of Vietnam. We develop some Matlab programs to find the coefficients of splines and calculate the values of the interpolation functions at specific points. Using the obtained interpolation function, some missing values in the data on income and expenditure per capita in the Southeast region of Vietnam in 2019 and 2021 are estimated. Fur-ther-more, some unknown data on rice productivity and cultivation area are obtained in a similar manner. A good agreement between the calcu-lated values and actual values are found.