Curve Fitting Using Levenberg-Marquardt Algorithm for Nonlinear Least Squares

This article explores how to implement the Levenberg-Marquardt (LM) algorithm for nonlinear least squares curve fitting using MATLAB. The LM algorithm combines gradient descent and Gauss-Newton methods to efficiently solve nonlinear optimization problems. We will detail the algorithm's mathematical foundation, implementation steps, and provide practical MATLAB code examples with sample datasets to demonstrate proper usage. The implementation typically involves defining the objective function, calculating Jacobian matrices, and iteratively updating parameters using the LM damping factor. Key MATLAB functions like lsqnonlin will be discussed alongside custom implementation approaches. We will also analyze the algorithm's advantages in convergence stability and disadvantages in computational complexity, along with strategies for selecting optimal parameters such as initial guesses and termination tolerances. This guide aims to provide valuable insights for researchers and engineers working with MATLAB-based nonlinear optimization and curve fitting applications.