Implementation of Newton Interpolation Algorithm in MATLAB

In numerical analysis, Newton interpolation algorithm is a method for constructing interpolation polynomials. This polynomial can approximate the functional relationship between dependent and independent variables. Using Newton interpolation, we can estimate function values through known data points. The degree of the interpolation polynomial depends on both the number of known data points and the polynomial order. The algorithm employs divided differences to build the polynomial incrementally, making it computationally efficient when adding new data points. Due to its high accuracy and user-friendly implementation, Newton interpolation is widely applied across various fields including physics, engineering, and economics. The MATLAB implementation typically involves calculating divided difference coefficients and evaluating the nested polynomial form using Horner's method for optimal performance. When an independent variable value is input, the Newton interpolation algorithm computes the corresponding approximate value of the dependent variable through polynomial evaluation.