Expanded Michalik continued fraction interpolation and optimization for nonlinear function approximation

This paper presents an improved method for Michalik continued fraction interpolation, aimed at enhancing the accuracy of computation and numerical stability. The proposed approach involves adding new interpolation nodes to the existing ones and calculating the function values of these additional nodes using a recursive formula, thereby optimizing the overall interpolation process. Furthermore, an error analysis was conducted for the added nodes to determine the optimal configuration, achieving the best possible approximation performance. Experimental results indicate that the enhanced interpolation method shows superior accuracy and better applicability for approximating nonlinear functions. Therefore, this extended interpolation method offers a more effective solution for the interpolation of complex functions and has potential applications in engineering and scientific computations.