By applying the Fourier analysis, we study the spectral properties of R- filters. Further, we prove that R-filters are a generalization of least squares polynomial adjustment, and we give the geometric interpretation of R-filters.
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, exact interpolating methods are often proposed for the exact results and approximate interpolating methods for the ap- proximate ones. In this paper, the authors study how to obtain exact interpolation polynomial with rational coefficients by approximate interpolating methods.
