MATLAB Curve Fitting Implementation with Code Examples

MATLAB serves as a powerful mathematical computing tool that offers multiple curve fitting methods, making it particularly suitable for handling experimental or engineering data fitting problems. Below are several common curve fitting implementation approaches with code-related descriptions: Polynomial Fitting with polyfit Function The fundamental approach uses polyfit for polynomial fitting. This function implements the least squares algorithm, requiring only input data points (x/y coordinates) and the desired polynomial degree to return fitting coefficients. While higher-degree polynomials can achieve better data fitting, users should be cautious of overfitting issues. Example implementation: p = polyfit(x, y, n) where n represents the polynomial order, and the output p contains coefficients from highest to lowest power. Interactive cftool Tool For users unfamiliar with command-line operations, MATLAB's Curve Fitting Toolbox (cftool) provides a graphical interface. Simply import data to select from 20+ built-in models (exponential, Fourier series, etc.), observe fitting results in real-time, and export generated code. The toolbox automatically generates optimization algorithms and validation metrics behind the scenes. Custom Function Fitting When fitting special function forms is required, use fittype to define function templates (e.g., y = a*exp(b*x)) combined with fit function for nonlinear least squares fitting. This method requires preliminary mathematical understanding of the model. Implementation example: ftype = fittype('a*exp(b*x)'); fit_result = fit(x, y, ftype). Practical applications typically involve using plot to create comparison graphs between original data and fitted curves, evaluating fitting quality through metrics like R-square. For noisy data, preprocess with smoothdata function before fitting to enhance results. Key validation code: rsquare = 1 - sum((y - y_fit).^2)/sum((y - mean(y)).^2).