Stellenbosch University
Applied Mathematics


Aankondigings / Announcements

  • Contrary to what was announced at the second test, we are not at liberty to post final marks nor marks for the second test here. You will get these marks through the official channels. (Depending on whether your department has a moderation process for these papers, this may take a while.) Should you need the third opportunity to pass the module, you will be informed by an email to your sun address before Friday 8 June. (For details of the third opportunity, see below.) Please do not send email to your instructors to enquire about your mark.
  • All assignment marks now available here. This is your final chance to look it over and let us know if there are mistakes. Copies of Assignment 6 can be picked up from the alphabetical boxes at Applied Math
  • For students who do not have the required 50 percent average at the end of the term, a third test opportunity will be available on Tuesday 19 June in A308 at 9:00. This 2-hour test will cover all the work of the semester (both terms), and it will replace the lowest score of the two prior tests. Should a passing score thus be obtained, a final mark of 50 percent will be assigned, regardless of the actual test mark.
  • A flow chart for deciding on an iterative method for Ax = b can be found here (taken from CULA Tools)
  • Derivation of the formula for the SSOR preconditioner as given on p.347 of the text.
  • Handout that demonstrates conjugate directions vs steepest descent directions can be found here.

  • This course assumes some previous experience with MATLAB or Python. If you need a refresher for MATLAB we strongly suggest reading the introductory slides (afr & eng) and/or completing the (free) online MATLAB Onramp (which takes about 2 hours). Note that MATLAB is now FREE for all SU students! Download instructions here.


Dosent / Lecturer

First term:
Second term:


Rooster / Timetable

  • Monday 11:00 @ M203
  • Wednesday 09:00 @ M203
  • Thursday 12:00 @ M203


Inligtingstukke / Information Sheets

  • Information sheet available here.


Notas / Notes


Opdragte / Assignments


Tests

  • Test 01 2018 and solutions


    2018 Skedule / Schedule (tentative)

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

    Week 2 (Chapter 2)
    • Intro to conditioning of linear systems. (Undergraduate slides: eng / afr)
    • Solving linear systems
    • Elimination
    • LU factorization

    Week 3

    Week 4

    Week 5 (Chapter 3)
    • Chapter 3: Least squares
    • Normal equations
    • QR Factorization
    • Householder transformation
    • Givens rotations
    • Gram-Schmidt

    Week 6 (Chapter 4)
    • Review of eigenvalues, eigenvectors, diagonalization (Undergraduate slides: eng / afr)
    Week 7
      Revision class (and public holiday)

    Test week and Term break

    Week 8
    • Similarity transformations, power iteration and its variants
    • Rayleigh-quotient iteration, QR iteration
    • Some implementation details of QR iteration, Hessenberg factorization

    Week 9 (Chapter 11)
    • Arnoldi and Lanczos algorithms
    • Arnoldi & Lanczos continued

    Week 10
    • Model problem, sparse matrices PDE model problem. Related undergraduate notes.
    • Iterative methods for Ax = b: splitting methods; convergence
    • Jacobi, Gauss-Seidel, SOR iterations (classroom demo).

    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

    Week 13


    MATLAB Kodes / MATLAB Codes