Stellenbosch University
Applied Mathematics


Aankondigings / Announcements

Summary of semester marks (now including Assignment 6 and Test 02 marks ). Please send Email if you see mistakes. Note that these marks are tentative and subject to moderation. Final marks will be made available on the university system in due course. If you have not received email from either lecturer then you are not eligible for any second opportunity tests.

Marked Assignment 6 available in the alphabetical boxes on the 4th floor


Dosent / Lecturer

First term:
Second term:


Rooster / Timetable

  • Tuesday 13:00 @ M203
  • Wednesday 10:00 @ M203
  • Thursday 10:00 @ M203


Inligtingstukke / Information Sheets

Information Sheet


Notas / Notes

MATLAB Intro and accompanying lecture slides Afrikaans / English

Chapter 1; Lecture Slides 1 (Background Material = Recommended Reading)

Chapter 2; Lecture Slides 2 (Linear Systems)

Chapter 3; Lecture Slides 3 (Least Squares)
(Undergraduate notes on least squares: English /Afrikaans)

Chapter 4; Lecture Slides 4 (Eigenvalues)

Chapter 11 (pp.335-350); Lecture slides 11 (long) / (short) (Direct and Iterative Methods for Sparse Systems)


Opdragte / Assignments


2017 Skedule / Schedule (tentative)

Week 1 (Jan 31, Feb 1,2):

  • Fundamentals (Undergraduate slides: eng1, eng2 / afr1, afr2)
  • Linear systems
  • Existence and uniqueness of solutions
  • Vector and matrix norms
  • Intro to conditioning of linear systems. (Undergraduate slides: eng / afr)

Week 2 (Feb 7,8,9):

  • Solving linear systems
  • Elimination
  • LU factorization
  • Gaussian elimination

Week 3 (Feb 14,15,16):

  • Instability and error growth factor
  • Pivoting
  • Algorithmic complexity
  • Sherman-Morrison formula

Week 4 (Feb 21,22,23):

  • Special types of linear systems
  • Cholesky factorization
  • Chapter 3: Least squares
  • Normal equations

Week 5 (Feb 28, Mar 1,2):

  • Conditioning of LS problem
  • QR Factorization
  • Householder transformation
  • Givens rotations

Week 6 (Mar 7,8,9):

  • Gram-Schmidt
  • Singular value decomposition (SVD)

Term break

Week 7 (Mar 22, 23):

  • Review of eigenvalues, eigenvectors, diagonalization (Undergraduate slides: eng / afr)
  • Review continued

Week 8 (Mar 28, 29, 30) (no live lectures)

Week 9 (Apr 4, 5, 6)

  • Arnoldi and Lanczos algorithms
  • Arnoldi & Lanczos continued
  • Model problem, sparse matrices PDE model problem. Related undergraduate notes.

Week 10 (Apr 18, 19, 20)

  • Direct methods for sparse systems; reordering (classroom demo)
  • Iterative methods for Ax = b: splitting methods; convergence
  • Jacobi, Gauss-Seidel, SOR iterations (classroom demo).

Week 11 (Apr 25, 26; no class on 27)

  • Jacobi, Gauss-Seidel, SOR iterations (continued)
  • Rate-of-convergence for the 2D Model Problem

Week 12 (May 2, 4; no class on 3)

Week 13 (May 9, 10; 11)


MATLAB Kodes / MATLAB Codes


2016 Skedule / Schedule (for reference)

Week 1 (Feb 2&4): Linear systems; existence and uniqueness of solutions; vector and matrix norms; intro to conditioning of linear systems. Undergraduate slides: English / Afrikaans

Week 2 (Feb 9&11): Conditioning (cont); the A = LU and PA = LU factorizations.

Week 3 (Feb 16&18): Instability of GE and the growth factor; Complexity of matrix computations; Sherman-Morrison formula

Week 4 (Feb 23&25): Symmetric positive definite systems; Cholesky factorization; Review of the least squares problem; Normal equations. Undergraduate notes on least squares: English / Afrikaans

Week 5 (Mar 1&3): Least squares problem (cont); Orthogonal matrices; QR factorization with Gram-Schmidt.

Week 6 (Mar 8&10): Gram-Schmidt; Solving the LS problem with Householder. Geometry of a Householder transformation (diagram).

Test week & Easter break

Week 7 (Mar 29&31): Eigenvalues: intro, similarity, power iterations, Rayleigh-Quotient iteration. Properties of symmetric/Hermitian matrices

Week 8 (Apr 5&7): QR iteration. Lanczos & Arnoldi algorithms.

Week 9 (Apr 12&14): PDE model problem. Related undergraduate notes. Direct methods for sparse matrices: reordering and bandwidth reducing algorithms. Intro to iterative methods.

Week 10 (Apr 19&21): Jacobi, Gauss-Seidel, SOR, Incomplete Cholesky iterations. Convergence rates and complexity for the 2D model problem.

Week 11 (Apr 26&28): Convergence rates and complexity (cont). Quadratic forms. Solving s.p.d. systems with minimization methods. Method of steepest descents.

Week 12 (May 3; no class on May 5): Conjugate gradient method (CG).

Week 13 (May 10 & 12): Preconditioned CG method. Error estimates for CG. Nonsymmetric variants of CG.