Methods for Nonlinear Function Fitting in MATLAB

In MATLAB, nonlinear function fitting is primarily achieved using the `lsqcurvefit` function. This function implements the least squares optimization method to fit data to specified nonlinear models by minimizing the sum of squared residuals between the model predictions and observed data.

The standard workflow for `lsqcurvefit` involves three key steps: first, defining the nonlinear model function (typically as a separate function file or anonymous function); second, providing initial parameter estimates to guide the optimization algorithm; and finally, executing the function with appropriate data inputs. MATLAB's optimization algorithms automatically adjust parameters to minimize the objective function using trust-region or Levenberg-Marquardt algorithms.

Beyond `lsqcurvefit`, MATLAB offers specialized alternatives like `fitnlm` (for creating nonlinear regression models with statistical outputs) and `nlinfit` (for basic nonlinear least-squares fitting with robust options). These tools support various applications in scientific computing, data analysis, and engineering modeling, providing features like Jacobian calculation, confidence intervals, and robust weighting schemes for handling outliers.