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;
  • The Smart Money’s on Numerical Analysts
  • Open problems in Matrix Theory
  • Open problems in Numerical Linear Algebra
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• 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