Obtaining exact interpolation multivariate polynomial by approximation

In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In order to improve the situation, exactly interpolating methods are often proposed for the exact results and approximate interpolating methods for the approximate ones. In this paper, we study how to obtain exact interpolation polynomial with rational coefficients by approximate interpolating methods.