Numerical Linear Algebra
Numerical Linear Algebra involves the development, analysis, and implementation of computational algorithms for solving linear algebra problems. These problems frequently arise in applications such as physical simulations, signal processing, neural network design, and many more. This course focuses on numerical methods for linear systems and eigenvalue problems. We will study both direct and iterative approaches, including Gaussian Elimination, LU Factorization, Jacobi and Gauss-Seidel Iterations, Steepest Descent, Conjugate Gradient, the Power Method, and more. Additional key topics include matrix decompositions, matrix/vector norms, computational efficiency, and stability. MATLAB programming skills will be introduced and developed throughout the semester. (MATH 0122 and MATH 0200)