The focus of this course will be on learning and developing stable algorithms for various matrix problems as mentioned below.

Solving Linear systems: $LU$, $LL^T$

Least Square and least norm problem: $QR$ decomposition

Singular Value Decomposition: $U\Sigma V^T$

Eigen Value Decomposition: $X\Lambda X^{1}$

Iterative methods: Krylov subspace methods including Lanczos, Arnoldi, Conjugate Gradient, GMRES.

Preconditioning and structured matrix computations.
However, before we proceed with the above, we will first look at three crucial aspects that are important for any computing course. These are: