Iterative Methods for Linear Equations

This lecture covers iterative methods for solving systems of linear equations, focusing on Richardson's method and convergence analysis. It explains the use of preconditioning matrices and the importance of choosing a good preconditioner. The lecture also delves into Gauss-Seidel and the convergence analysis of Richardson's method. It discusses error control, stopping criteria, and the properties of positive definite matrices. The lecture concludes with the design of iterative methods to minimize energy functions and approximate solutions.