Nonlinear Least Squares Fitting with MATLAB Implementation

In this experiment, we will utilize MATLAB to conduct nonlinear least squares fitting for mathematical modeling and experimentation. Nonlinear least squares methods enable more accurate data fitting, leading to superior model results. We will implement various fitting functions using MATLAB's optimization toolbox and compare their performance characteristics while analyzing their respective advantages and limitations. Our implementation will involve key MATLAB functions such as lsqnonlin for nonlinear least-squares problems and lsqcurvefit for curve fitting applications. We will investigate strategies for selecting appropriate initial parameter values and fitting algorithms (such as Levenberg-Marquardt or Trust-Region algorithms) to achieve optimal fitting results. The experimental process will include evaluating convergence criteria, residual analysis, and goodness-of-fit metrics like R-squared values. Through these analytical procedures, we will gain comprehensive understanding of nonlinear least squares fitting principles and their practical applications, establishing a solid foundation for future mathematical modeling and experimental work. The methodology will cover error minimization techniques, Jacobian matrix computations, and handling of local minima challenges common in nonlinear optimization problems.