From Linear Equations to Learning Systems: Gauss–Seidel Method in AI and Machine Learning.
Usually, students in Computer Science and Engineering (CSE) are taught the Gauss-Seidel iterative method as part of numerical methods for solving linear systems. However, this traditional method actually has a direct association with AI and machine learning (ML) algorithms of today. Gaining an understanding of Gauss-Seidel might help you better grasp optimization, convergence, and iterative learning that drive the intelligent systems of the present day. What is the Gauss-Seidel methodology? The Gauss-Seidel method is an iterative (step-by-step) method to solve a system of linear equations: 𝐴𝑥 = 𝑏 . where A is a square matrix, x is the vector of unknowns, and b is the constant vector. Instead of direct methods (such as Gaussian elimination), Gauss-Seidel step by step refines the guess of the solution through an approximation process until the solution levels off at the convergence. Iteration formula: For a system with equations: Numerical Example: Ste...