Stellenbosch University
Applied Mathematics


Aankondigings / Announcements

  • Marks for Assignment 5 available here. Marks for Assignment 6 will not be available before the test on May 30.
  • Solutions to both Assignments 5 and 6 available below. Marked assignments 5 can be picked up in the alphabetical boxes at Applied Math, 3rd floor.
  • The second test is scheduled for Wednesday 30 May at 9:00. It will cover all the material of Weeks 6 through 13, as summarized in the schedule below. To help you prepare, here is the 2017 test.
  • There is no subminimum enforced for the second test. Skipping it is not recommended, however, as some assignment marks will only be available after the test. Predicting a final mark is therefore risky.
  • For students who do not have the required 50 percent average at the end of the term, a third test opportunity will be available in the week of 18-22 June (time and date to be decided). 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