Iterative Methods for Linear Equations

This lecture covers iterative methods for solving systems of linear equations, focusing on Jacobi and Gauss-Seidel methods. It explains the convergence criteria, decomposition methods, and the Jacobi method's general formula. The lecture also discusses the Gauss-Seidel method, quadratic forms, and the conjugate gradient method. It delves into the idea of the algorithm, steepest descent method, and improving it by searching along mutually orthogonal directions. The conjugate gradient idea is introduced, emphasizing A-orthogonality. The lecture concludes with the conjugate gradient algorithm, its convergence, and its application in classical force fields and potential energy surfaces of complex biological molecules.