MATLAB Implementation of Interpolation Algorithms and Curve Fitting

This article presents MATLAB implementations of interpolation algorithms and curve fitting techniques, which serve as highly valuable computational tools. Interpolation algorithms are primarily used for estimating missing data points between known values, while curve fitting aims to find optimal mathematical functions that best describe data patterns. In practical applications, MATLAB provides essential functions for these operations: interp1 for 1D interpolation with methods like linear, spline, and cubic interpolation; polyfit for polynomial curve fitting with least-squares optimization; and fit for custom model fitting using specified equation forms. These tools find extensive applications across data processing, signal analysis, image processing, and scientific computing domains. It's noteworthy that while MATLAB offers powerful built-in functions, users should consider its computational limitations when handling large datasets, as performance may decrease with significant data volumes. Therefore, practical implementation requires evaluating these constraints and selecting the most appropriate tools based on specific application requirements, potentially combining MATLAB with optimized algorithms or alternative platforms for large-scale computations.