Convergence of Gauss-Seidel Method | Numerical Methods in Hindi/Urdu | Hassaan Ghazi Mathematics

In this video, we will study the Convergence of the Gauss-Seidel Iterative Method step by step. Convergence is the key factor in deciding whether an iterative method will give the correct solution or not. Without convergence, the method may diverge and fail to solve the system of equations. We’ll cover: ✔️ What convergence means in iterative methods ✔️ Convergence criteria for the Gauss-Seidel Method ✔️ The role of diagonal dominance in convergence ✔️ Spectral radius condition and its importance ✔️ Comparison of convergence between Jacobi and Gauss-Seidel Methods ✔️ Worked examples showing when Gauss-Seidel converges or diverges This tutorial is specially designed for Engineering, Mathematics, and Computer Science students who want to master the concepts of Numerical Analysis. By the end of this lecture, you will clearly understand why convergence is necessary, how to check convergence, and why Gauss-Seidel often converges faster than Jacobi. 👉 Don’t forget to watch the related videos on Jacobi Iterative Method, Gauss-Seidel Method, SOR Method, and Convergence of Jacobi Method to complete the entire series. 📚 Channel: Hassaan Ghazi Mathematics 💡 Subscribe to the channel and turn on the bell icon to continue learning Numerical Methods in Hindi/Urdu with easy explanations. #GaussSeidelMethod #Convergence #NumericalMethods #NumericalAnalysis #EngineeringMathematics #IterativeMethods #GaussSeidelConvergence #JacobiVsGaussSeidel #HassaanGhaziMathematics #EngineeringStudents #MathTutorial #StudyWithMe