Stellenbosch University
Applied Mathematics


Aankondigings / Announcements

Test 01 on Tuesday 14 March @ 8AM (Venue TBC).

ASSIGNMENT 02 CORRECTIONS

  • For Problem 3(c) rather change the a 3,3 entry to 6.
  • Problem 4 is optional.


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

Assignment 1 (handed in on Feb 17)
Solutions 1
Assignment 2 (handed in on March 02)


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)


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.