Curve Fitting MATLAB Program

Curve fitting is a powerful data analysis feature in MATLAB that enables users to find the most appropriate mathematical function for given data points. This technique is widely applied in engineering, scientific research, and financial modeling to uncover underlying patterns in data.

Implementing curve fitting in MATLAB typically involves several key steps. First, you need to prepare input data consisting of observed values for independent and dependent variables. MATLAB provides multiple fitting functions where you can select appropriate algorithms based on data characteristics. Common fitting methods include polynomial fitting (using polyfit function), exponential fitting (fit function with 'exp1' model), and sinusoidal curve fitting, each suitable for different data distribution patterns.

During the fitting process, MATLAB automatically calculates parameters for the fitted curve to minimize errors between the curve and data points. Users can specify fitting order or complexity using parameters like polynomial degree in polyfit, balancing fitting accuracy against overfitting risks. After completion, MATLAB generates goodness-of-fit statistics like R-squared and RMSE to evaluate fitting quality.

Beyond basic fitting capabilities, MATLAB supports custom fitting functions through fittype function for specialized requirements. Users can visualize fitting results using plot functions to visually compare raw data with fitted curves. Additionally, MATLAB's fitting tools provide confidence intervals for fitted parameters using confint function, indicating parameter estimation reliability.

For higher precision applications, MATLAB allows adjustment of fitting algorithm parameters such as convergence tolerance (TolFun) and maximum iterations (MaxIter) through optimset options. These advanced features make MATLAB a robust tool for handling complex curve fitting problems.