Iterative Least Squares Algorithm for Curve Fitting

This article explores the implementation of curve fitting using the iterative least squares algorithm. Curve fitting is the process of constructing a curve that best fits a series of discrete data points, aiming to minimize the error between the curve and the known data points. The iterative least squares method, a widely used approach in curve fitting, employs successive optimization iterations to progressively approach the optimal solution. The algorithm typically involves initial parameter estimation followed by iterative refinement using gradient descent or Gauss-Newton methods, where each iteration recalculates weights based on residual errors. Key implementation aspects include defining the objective function, calculating Jacobian matrices for parameter updates, and setting convergence criteria. Through this method, we can achieve higher accuracy in curve fitting results, thereby enabling better data understanding and analysis. Code implementation often involves matrix operations for efficient computation of parameter updates and residual calculations.