Least Squares Method with Nonlinear and Linear Fitting

In this article, we will discuss the application of the least squares method, which includes both nonlinear and linear fitting approaches. The least squares method is a widely used statistical technique for solving practical problems, capable of fitting various curves and surfaces. We will introduce the theoretical foundations of least squares along with practical application examples. These examples include real-world implementations of curve and surface fitting using least squares, demonstrating how to apply this method to solve practical problems. Through this article, you will understand the fundamental concepts and applications of least squares, as well as its significance in real-world scenarios. The implementation typically involves optimization algorithms like gradient descent for nonlinear cases and matrix operations (using QR decomposition or singular value decomposition) for linear systems, with key functions including cost function minimization and parameter estimation through normal equations.