Iterative Methods for Linear Equations

This lecture covers iterative methods for solving systems of linear equations, focusing on the concept of energy function and the unique minimum solution. It introduces the design of iterative methods to approximate solutions, rather than computing directly. The lecture discusses the properties of symmetric positive definite matrices and the application of iterative methods to minimize errors. It also explores the gradient method, specifically the steepest descent method, for solving linear equations. The lecture concludes with the theorem stating the convergence of the gradient method for solving linear equations with symmetric positive definite matrices.