Nonlinear Function Curve Fitting Implementation

When performing curve fitting for nonlinear functions, several critical factors must be considered. First, we need to conduct thorough data analysis to determine the most suitable type of fitting curve, which may involve examining data patterns and selecting appropriate nonlinear models such as exponential, logarithmic, or polynomial functions. The implementation utilizes MATLAB's m-file programming approach, employing key optimization functions like lsqcurvefit or fminsearch for parameter estimation. These algorithms work by minimizing the sum of squared residuals between the experimental data and the fitted curve through iterative refinement processes. To ensure optimal fitting results, experimental data requires preprocessing and optimization. This includes handling missing values, removing outliers using statistical methods like the 3-sigma rule, and normalizing data when necessary. The txt file format allows for efficient data import using MATLAB's readtable or load functions, ensuring data integrity through proper validation checks. The fitting process involves parameter initialization, iterative optimization with convergence criteria, and residual analysis. Key implementation aspects include setting appropriate tolerance levels, maximum iteration limits, and choosing between different optimization algorithms based on the problem characteristics. Finally, we evaluate the fitting results through statistical metrics such as R-squared values, root mean square error (RMSE), and visual comparison with original data. The implementation includes validation routines to assess goodness-of-fit and generate comparison plots, ensuring the reliability and accuracy of the fitted model through comprehensive diagnostic checks.