Скачать или смотреть Conjugate Gradient Method (Quadratic) | Numerical Methods in Hindi/Urdu | Fletcher-Reeves

In this video, we will study the Conjugate Gradient Method, one of the most powerful and efficient iterative techniques in Numerical Methods used to solve large systems of linear equations. The Conjugate Gradient Method is especially effective for symmetric and positive definite matrices and is widely used in scientific computing and engineering applications.

Unlike classical iterative methods such as Jacobi, Gauss-Seidel, and SOR, the Conjugate Gradient Method converges in fewer iterations and is well-suited for large sparse systems.

We’ll cover:
✔️ What is the Conjugate Gradient Method?
✔️ Conditions for applying the CG Method
✔️ Basic idea of conjugate directions
✔️ Step-by-step algorithm of the Conjugate Gradient Method
✔️ Relation with Gradient Descent Method
✔️ Solved numerical example for better understanding
✔️ Advantages, limitations, and convergence behavior

This lecture is specially designed for Engineering, Mathematics, and Computer Science students who want to understand advanced Iterative Methods in Numerical Analysis. The explanation is given in Hindi/Urdu, making complex concepts easy to understand.

By the end of this video, you will clearly understand how the Conjugate Gradient Method works, why it is faster than classical methods, and where it is most effectively used in real-world problems.

📚 Channel: Hassaan Ghazi Mathematics
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