MATLAB Implementation of Quadratic Interpolation Method

This content discusses the MATLAB implementation of quadratic interpolation methods from optimization theory textbooks. These methods are commonly used for function approximation in optimization problems and have wide practical applications. The implementation includes two main approaches: parabolic interpolation and three-point quadratic interpolation, with specific usage details available in the program documentation. The key difference between these methods lies in how they perform interpolation between given data points and how they fit functions when higher accuracy requirements are needed. In MATLAB implementation, the parabolic interpolation method typically uses a single quadratic function to approximate the objective function, while the three-point method selects three optimal points to construct the interpolation polynomial. Both methods employ MATLAB's matrix operations and polynomial fitting functions like polyfit for efficient computation. Overall, quadratic interpolation provides a robust tool that delivers excellent performance in optimization problems, particularly in line search algorithms where it helps locate minima with quadratic convergence properties.