Stellenbosch University
Applied Mathematics


Aankondigings / Announcements

  • Proof of PA = LU factorization mentioned in class availabale here.
  • Assignment 02 is available below.


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


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
  • Sherman-Morrison formula
  • Special types of linear systems
  • Cholesky factorization

Week 5 (Chapter 3)
  • Chapter 3: Least squares
  • Normal equations
  • Conditioning of LS problem
  • QR Factorization

Week 6
  • Householder transformation
  • Givens rotations
  • Gram-Schmidt

Test week and Term break

Week 7 (Chapter 4)
  • Review of eigenvalues, eigenvectors, diagonalization (Undergraduate slides: eng / afr)
  • Review continued

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
  • Model problem, sparse matrices PDE model problem. Related undergraduate notes.

Week 10
  • 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
  • Jacobi, Gauss-Seidel, SOR iterations (continued)
  • Rate-of-convergence for the 2D Model Problem

Week 12

Week 13


MATLAB Kodes / MATLAB Codes