Stellenbosch University
Applied Mathematics

Announcements

  • Final marks here. (Apologies for the delay: My understanding was that the M&M Dept would distribute the marks.)
  • Those who have access to A3 have been contacted via email.
  • Marks for assignment 06 available here.
  • Updated blooper from lecture May 9th here. (Page 11.)
  • Some further reading on conjugate gradients available here: cg1.pdf, cg2.pdf, cg_lev.pdf, cgsau.pdf, cg_iteration.png.
  • Hand out on the 1D and 2D model problems discussed in class here.
  • Prof Hale's lecture notes 1-9, 10-16, and 17-21, 22, and 23-29.
  • MATLAB

    • This course assumes some previous experience with MATLAB (or Python).
    • MATLAB is now FREE for all SU students! Download instructions here.
      Alternatively, you can use MATLAB in your browser! (But this may be slower.)
    • I strongly recommend completing the (free) online MATLAB Onramp as a refresher.

    Lecturer

    Timetable

    All lectures will be in the Paul Sauer lecture theatre (1006 Forestry Science)
    • Monday @ 11
    • Wednesday @ 1
    • Thursday @ 10

    Information Sheets

    • Information sheet available here.

    Notes

    Assignments

    Assignment Due date Solutions Marks
    Assignment 1 18/02/2019 Solutions 1 Marks 1
    Assignment 2 04/03/2019 Solutions 2 Marks 2
    Assignment 3 13/03/2019 Solutions 3 Marks 3
    Assignment 4 15/04/2019 Solutions 4 Marks 4
    Assignment 5 29/04/2019 Solutions 5 Marks 5
    Assignment 6 13/05/2019 Solutions 6 Marks 6

    Schedule

    Week 1 (Chapter 1)
    • Fundamentals (Undergraduate slides: eng1, eng2 / afr1, afr2)
    • Linear systems; Existence and uniqueness of solutions

    Week 2 (Chapter 2)
    • Vector and matrix norms
    • conditioning of linear systems. (Undergraduate slides: eng / afr)
    • Solving linear systems

    Week 3

    Week 4

    Week 5
    • Normal equations
    • QR Factorization
    • Householder transformation
    • Givens rotations
    • Notes 10--16

    Week 6
    • Revision
    • Test week

    Week 7
    • Test week

    Week 8 (Chapter 4)
    • Review of eigenvalues, eigenvectors, diagonalization, similarity transforms (Undergraduate slides: eng / afr)
    • Power iteration and its variants, Rayleigh-quotient iteration

    Week 9
    • QR iteration
    • Some implementation details of QR iteration, Hessenberg factorization
    • Arnoldi and Lanczos algorithms
    • Notes 17--21

    Week 10 (Chapter 11)
    • Model problem, sparse matrices. Related undergraduate notes. Notes 22
    • Iterative methods for Ax = b: splitting methods; convergence
    • Jacobi, Gauss-Seidel, SOR iterations.

    Week 11
    • Jacobi, Gauss-Seidel, SOR iterations (continued)
    • Incomplete LU and Cholesky
    • Minimization methods for Ax = b when A is s.p.d.

    Week 12
    • Method of steepest descent
    • Method of conjugate gradients

    Week 13
    • Convergence of CG
    • Pre-conditioned conjugate gradient method.
    Week 14
    • MINRES and GMRES
    • Rate-of-convergence for the 2D Model Problem
    • Notes 23--29