自适应Newton-Thiele有理插值及应用
Adaptive Newton-Thiele's rational interpolation and its application
李麟 1檀结庆 1邢燕1
作者信息
- 1. 合肥工业大学数学学院,安徽合肥 230601
- 折叠
摘要
二元连分式插值是二元有理插值的重要组成部分;文章在前人研究的基础上,对Newton-Thiele有理插值构造过程进行改进.针对Newton-Thiele有理插值在插值过程出现逆差商不存在的情况,传统的解决方法是将相应的Thiele型插值连分式转换为Newton插值多项式,然而该处理方法会导致计算复杂度的增加.借鉴相关文献在一元有理插值上的选点方法,文章给出一种带终止条件的自适应贪婪选点算法,即在给定插值点中根据自适应条件筛选出局部点对函数进行构造,以提高Newton-Thiele有理插值函数构造过程的稳定性,提升运算效率.对非线性函数的插值结果表明:该算法的插值效果较好、误差较小;同时将该算法应用到图像修复中,并与其他相关算法的修复效果进行对比,进一步验证了该算法的有效性.
Abstract
Binary continued fraction interpolation plays an important role in the field of binary rational interpolation functions.Based on previous studies,this paper improves Newton-Thiele's rational in-terpolation in practical application.In the construction of Newton-Thiele's rational interpolation,there are situations where the inverse differences do not exist.In traditional methods,when the in-verse differences do not exist,the corresponding Thiele-type continued fraction is replaced by a New-ton-type polynomial to solve this problem.However,this processing method leads to an increase in computational complexity.Drawing inspiration from the point selection methods in univariate rational interpolation in relevant literature,the paper explores a Newton-Thiele's rational interpolation algo-rithm based on adaptive greedy point selection strategy with termination conditions.By selecting par-tial points among the given points based on adaptive conditions,this algorithm can improve the stabili-ty of the construction process of Newton-Thiele's rational interpolation function and improve the effi-ciency of computation.Through nonlinear function interpolation,it is proved that the algorithm can produce favorable interpolation effect and maintain the error at a low level.Meanwhile,in the applica-tion of image inpainting,the algorithm is compared with other related algorithms to further verify the effectiveness of the algorithm.
关键词
连分式/逆差商存在性/Newton-Thiele有理插值/自适应贪婪算法/图像修复Key words
continued fractions/existence of inverse difference/Newton-Thiele's rational interpola-tion/adaptive greedy algorithm/image inpainting引用本文复制引用
基金项目
国家自然科学基金资助项目(62172135)
出版年
2024
NETL
NSTL
维普
万方数据