Iterative Methods for Linear Equations

This lecture covers iterative methods for solving systems of linear equations, including Jacobi and Gauss-Seidel methods, steepest descent, conjugate gradient method, and decomposition methods. It explains convergence criteria based on residue and increment, and the properties of Jacobi and Gauss-Seidel methods. The lecture also discusses the gradient of quadratic forms, convergence properties, and the conjugate gradient idea. Additionally, it explores the conjugate gradient algorithm, improving steepest descent, and the convergence of the conjugate gradient method. Finally, it touches on classical force fields and potential energy surfaces in complex atomistic systems, emphasizing the relevance of minima in the potential energy.