Nonlinear Function Fitting Methods in MATLAB: Key Functions and Implementation Approaches

This document provides an in-depth exploration of nonlinear function fitting procedures in MATLAB. MATLAB offers numerous built-in functions for fitting nonlinear models, including but not limited to least squares methods (implemented via lsqnonlin and lsqcurvefit), Newton-based optimization algorithms (fminunc, fmincon), and specialized fitting functions (nlinfit, fit from the Curve Fitting Toolbox). These functions employ various numerical optimization techniques to approximate nonlinear relationships in data, helping researchers better understand and interpret nonlinear system behaviors. Additionally, we discuss strategies for selecting appropriate fitting functions based on problem characteristics and address common challenges in nonlinear fitting such as overfitting (handled through regularization or cross-validation) and underfitting (resolved by model complexity adjustment). Through detailed examination of these aspects, users can develop deeper understanding and proficiency in implementing nonlinear function fitting methodologies using MATLAB's computational framework.