Comparative Analysis of Interpolation Methods: Linear Interpolation

Among various interpolation methods, linear interpolation, cubic polynomial interpolation, and polynomial fitting represent commonly used approaches in numerical analysis. Each technique exhibits distinct advantages and limitations that should be considered based on specific application requirements. Linear interpolation, for instance, while potentially less accurate than other methods, offers computational efficiency through simple linear calculations between adjacent data points - typically implemented using MATLAB's interp1 function with 'linear' method parameter. In contrast, cubic polynomial interpolation (often implemented via spline or interp1 with 'cubic' option) and polynomial fitting methods (using polyfit and polyval functions) generally provide superior accuracy and smoother curves, but demand greater computational resources due to higher-order polynomial calculations. To facilitate visual comparison and analysis, practitioners can plot both the interpolation results and original sampling points on a single graph using MATLAB's plotting functions, enabling direct evaluation of each method's performance characteristics relative to the underlying data distribution.