Date: July 29, 2019

• Course website and other logistics

• Motivation: Why do this course?
• You can make ₹'s, €'s $'s etc; The \$25,000,000,000 Eigenvector: The Linear Algebra Behind Google
• There are tons of open problems, when solved also turns out to be of practical relevance; </ul>

• 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:

• Floating point arithmetic

• Conditioning of a problem

• Stability of an algorithm