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 interpolation 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 inverse differences do not exist, the corresponding Thiele-type continued fraction is replaced by a Newton-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 algorithm based on adaptive greedy point selection strategy with termination conditions. By selecting partial points among the given points based on adaptive conditions, this algorithm can improve the stability of the construction process of Newton-Thiele's rational interpolation function and improve the efficiency 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 application of image inpainting, the algorithm is compared with other related algorithms to further verify the effectiveness of the algorithm.
Keywords: continued fractions; existence of inverse difference; Newton-Thiele's rational interpolation; adaptive greedy algorithm; image inpainting
合肥工业大学学报自科版