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