Linear Systems: Iterative Methods

This lecture covers the concept of linear systems and focuses on iterative methods such as gradient descent and conjugate gradient methods. It explains the stationary points of linear systems, the solution of Ax=b, and the properties of symmetric positive definite matrices. The lecture delves into the gradient method, steepest descent, and the Richardson's method, emphasizing the convergence to the minimum value. Additionally, it introduces the conjugate gradient method, highlighting its efficiency in finding the exact solution for a symmetric positive definite matrix. The lecture concludes with the discussion on the convergence of iterative methods and the importance of choosing the right preconditioner.