Syllabus

  • Basics and Linear Equation Solvers (6 lectures on LU, pivoting, nroms, floating point arithmetic, perturbation theory, backward error analysis and BLAS). Chapter 1 (except 1.5.1), Chapter 2 (except 2.2.1, 2.4.3, 2.4.4, 2.5, 2.5.1, 2.5.2, 2.7.5 )
  • The Linear Least Squares Problem (4 lectures on Normal Equations, QR, SVD, Rank-deficient case). Chapter 3 (except 3.3)
  • The Symmetric Eigenvalue Problem (approx. 6 lectures on Perturbation theory, bisection +inverse iteration, Rayleigh Quotient Iteration, QR Algorithm, Recent advances such as twisted factorizations, Jacobi method)
  • SVD Computations (approx. 2 lectures)
  • Iterative linear solvers (approx. 5 lectures on Jacobi, Gauss-Seidel, SOR, FFT, Krylov Subspace Based methods)
  • Sparse Eigenvalue Solvers (approx. 3 lectures on Lanczos)

    • Grading

  • 20% Homework
  • 40% Midterm
  • 40% Class Project