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Obtaining exact interpolation multivariate polynomial by approximation

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Abstract

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 approximate ones. In this paper, the authors study how to obtain exact interpolation polynomial with rational coefficients by approximate interpolating methods.

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Authors and Affiliations

  1. Laboratory of Computer Reasoning and Trustworthy Computation, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Yong Feng

  2. Laboratory for Automated Reasoning and Programming, Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu, 610041, China

    Xiaolin Qin

  3. Graduate University of Chinese Academy of Sciences, Beijing, 100049, China

    Xiaolin Qin

  4. Laboratory of Computer Reasoning and Trustworthy Computation, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Jingzhong Zhang

  5. Laboratory for Automated Reasoning and Programming, Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu, 610041, China

    Xun Yuan

Authors
  1. Yong Feng
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  2. Xiaolin Qin
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  3. Jingzhong Zhang
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  4. Xun Yuan
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Corresponding author

Correspondence to Xiaolin Qin.

Additional information

This research is supported by China 973 Program 2011CB302402, the Knowledge Innovation Program of the Chinese Academy of Sciences (KJCX2-YW-S02), the National Natural Science Foundation of China (10771205), and the West Light Foundation of the Chinese Academy of Sciences.

This paper was recommended for publication by Editor Ziming LI.

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Feng, Y., Qin, X., Zhang, J. et al. Obtaining exact interpolation multivariate polynomial by approximation. J Syst Sci Complex 24, 803–815 (2011). https://doi.org/10.1007/s11424-011-8312-0

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  • DOI: https://doi.org/10.1007/s11424-011-8312-0

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