Bivariate Thiele-Like Rational Interpolation Continued Fractions with Parameters Based on Virtual Points

doi:10.3390/math8010071

	Bivariate Thiele-Like Rational Interpolation Continued Fractions with Parameters Based on Virtual Points
	Zou, Le 1,2,3; Song, Liangtu 1,3; Wang, Xiaofeng 2; Chen, Yanping 2; Zhang, Chen 2; Tang, Chao 2
刊名	MATHEMATICS
	2020
卷号	8
关键词	Thiele-like rational interpolation continued fractions with parameters unattainable point inverse difference virtual point
DOI	10.3390/math8010071
通讯作者	Zou, Le(chenypo@hfuu.edu.cn) ; Wang, Xiaofeng(zhangchen@hfuu.edu.cn)
英文摘要	The interpolation of Thiele-type continued fractions is thought of as the traditional rational interpolation and plays a significant role in numerical analysis and image interpolation. Different to the classical method, a novel type of bivariate Thiele-like rational interpolation continued fractions with parameters is proposed to efficiently address the interpolation problem. Firstly, the multiplicity of the points is adjusted strategically. Secondly, bivariate Thiele-like rational interpolation continued fractions with parameters is developed. We also discuss the interpolant algorithm, theorem, and dual interpolation of the proposed interpolation method. Many interpolation functions can be gained through adjusting the parameter, which is flexible and convenient. We also demonstrate that the novel interpolation function can deal with the interpolation problems that inverse differences do not exist or that there are unattainable points appearing in classical Thiele-type continued fractions interpolation. Through the selection of proper parameters, the value of the interpolation function can be changed at any point in the interpolant region under unaltered interpolant data. Numerical examples are given to show that the developed methods achieve state-of-the-art performance.
资助项目	National Natural Science Foundation of China[61672204] ; National Natural Science Foundation of China[61806068] ; Key Scientific Research Foundation of Education Department of Anhui Province[KJ2018A0555] ; Key Scientific Research Foundation of Education Department of Anhui Province[KJ2018A0556] ; Key Scientific Research Foundation of Education Department of Anhui Province[KJ2019A0833] ; Natural Science Foundation of Anhui Provincial[1908085MF184] ; Natural Science Foundation of Anhui Provincial[1508085QF116] ; Key Technologies R&D Program of Anhui Province[1804a09020058] ; Major Science and Technology Project of Anhui Province[17030901026] ; Key Constructive Discipline Project of Hefei University[2016xk05]
WOS研究方向	Mathematics
语种	英语
出版者	MDPI
WOS记录号	WOS:000515730100037
资助机构	National Natural Science Foundation of China ; Key Scientific Research Foundation of Education Department of Anhui Province ; Natural Science Foundation of Anhui Provincial ; Key Technologies R&D Program of Anhui Province ; Major Science and Technology Project of Anhui Province ; Key Constructive Discipline Project of Hefei University
内容类型	期刊论文
源URL	[http://ir.hfcas.ac.cn:8080/handle/334002/103943]
专题	中国科学院合肥物质科学研究院
通讯作者	Zou, Le; Wang, Xiaofeng
作者单位	1.Chinese Acad Sci, Hefei Inst Phys Sci, Inst Intelligent Machines, Hefei 230031, Anhui, Peoples R China 2.Hefei Univ, Sch Artificial Intelligence & Big Data, Hefei 230601, Anhui, Peoples R China 3.Univ Sci & Technol China, Hefei 230026, Anhui, Peoples R China
推荐引用方式 GB/T 7714	Zou, Le,Song, Liangtu,Wang, Xiaofeng,et al. Bivariate Thiele-Like Rational Interpolation Continued Fractions with Parameters Based on Virtual Points[J]. MATHEMATICS,2020,8.
APA	Zou, Le,Song, Liangtu,Wang, Xiaofeng,Chen, Yanping,Zhang, Chen,&Tang, Chao.(2020).Bivariate Thiele-Like Rational Interpolation Continued Fractions with Parameters Based on Virtual Points.MATHEMATICS,8.
MLA	Zou, Le,et al."Bivariate Thiele-Like Rational Interpolation Continued Fractions with Parameters Based on Virtual Points".MATHEMATICS 8(2020).