Convergence of Jacobi Iterative Method | Numerical Methods in Hindi/Urdu | Hassaan Ghazi Mathematics

In this video, we will study the Convergence of the Jacobi Iterative Method in detail. Understanding convergence is extremely important in Numerical Methods, because not every iterative method gives the correct solution — it only works under certain conditions. We’ll discuss: ✔️ What does convergence mean in iterative methods? ✔️ Convergence criteria for the Jacobi Method ✔️ The concept of diagonal dominance ✔️ Spectral radius condition and its importance ✔️ Examples showing when Jacobi converges and when it fails ✔️ Relation of convergence with Gauss-Seidel and SOR Methods This lecture is specially designed for Engineering, Mathematics, and Computer Science students who want to gain a deeper understanding of Numerical Analysis. By the end of this tutorial, you will clearly understand why convergence is necessary, how to test it, and how it affects the accuracy of the Jacobi Iterative Method. 👉 Make sure to watch the previous videos on Jacobi Iterative Method, Gauss-Seidel Method, and SOR Method to build a strong foundation before diving into convergence analysis. 📚 Channel: Hassaan Ghazi Mathematics 💡 Subscribe to the channel and hit the bell icon to keep learning Numerical Methods in Hindi/Urdu in the most simple and clear way. #JacobiMethod #Convergence #NumericalMethods #EngineeringMathematics #NumericalAnalysis #IterativeMethods #JacobiConvergence #MathTutorial #HassanGhaziMathematics #EngineeringStudents #StudyWithMe #MathematicsHindiUrdu