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 ...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.展开更多
Numerical approximate computations can solve large and complex problems fast.They have the advantage of high efficiency.However they only give approximate results,whereas we need exact results in some fields.There is ...Numerical approximate computations can solve large and complex problems fast.They have the advantage of high efficiency.However they only give approximate results,whereas we need exact results in some fields.There is a gap between approximate computations and exact results. In this paper,we build a bridge by which exact results can be obtained by numerical approximate computations.展开更多
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...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.展开更多
基金Project supported by the National Basic Research Program of China (973 Program) (No. NKBRPC-2004CB318003)the Knowledge Innovation Program of the Chinese Academy of Sciences(No. KJCX2-YW-S02)the National Natural Science Foundation of China (No. 10771205)
文摘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.
基金This work was partially supported by China 973 Project (Grant No.NKBRPC-2004CB318003)the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No.KJCX2-YW-S02).
文摘Numerical approximate computations can solve large and complex problems fast.They have the advantage of high efficiency.However they only give approximate results,whereas we need exact results in some fields.There is a gap between approximate computations and exact results. In this paper,we build a bridge by which exact results can be obtained by numerical approximate computations.
基金supported by China 973 Frogram 2011CB302402the Knowledge Innovation Program of the Chinese Academy of Sciences(KJCX2-YW-S02)+1 种基金the National Natural Science Foundation of China(10771205)the West Light Foundation of the Chinese Academy of Sciences
文摘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.
