Abstract
Thiele-type continued fractions interpolation may be the classical rational interpolation and plays critical role in image interpolation and numerical analysis. Different from the traditional method, a new Thiele type continued fractions rational interpolation method with parameters was presented to address the interpolation problem efficiently. Firstly, in order to gain neat expressions in terms of inverse differences, we chose the multiplicity of the points strategically. Secondly, we constructed a univariate Thiele type continued fractions rational interpolation with parameters, which can satisfy the interpolation condition. We also discussed the interpolation algorithm, interpolation theorem. Numerical examples were given to show that the presented method achieves state-of-the-art performance.
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Acknowledgements
The authors would like to express their thanks to the referees for their valuable suggestions. This work was supported by the grant of the National Natural Science Foundation of China, Nos. 61672204, 61806068, the grant of Anhui Provincial Natural Science Foundation, Nos. 1508085QF116, 1908085MF184, the grant of the key Scientific Research Foundation of Education Department of Anhui Province, Nos. KJ2018A0555, KJ2018A0556, the grant of Major Science and Technology Project of Anhui Province, No. 17030901026, the grant of Key Technologies R&D Program of Anhui Province, No. 1804a09020058, the grant of Teaching Team of Anhui Province, No. 2016jxtd101.
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Zou, L. et al. (2019). Univariate Thiele Type Continued Fractions Rational Interpolation with Parameters. In: Huang, DS., Huang, ZK., Hussain, A. (eds) Intelligent Computing Methodologies. ICIC 2019. Lecture Notes in Computer Science(), vol 11645. Springer, Cham. https://doi.org/10.1007/978-3-030-26766-7_37
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DOI: https://doi.org/10.1007/978-3-030-26766-7_37
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