Announcements
MATLAB
 This course assumes some previous experience with MATLAB (or Python).

MATLAB is now FREE for all SU students! Download instructions here.
Alternatively, you can use MATLAB in your browser! (But this may be slower.)  I strongly recommend completing the (free) online MATLAB Onramp as a refresher.
Lecturer
 Prof Nick Hale, Office: A410, Email: nickhale@sun.ac.za
Timetable
All lectures will be in the Paul Sauer lecture theatre (1006 Forestry Science) Monday @ 11
 Wednesday @ 1
 Thursday @ 10
Information Sheets
 Information sheet available here.
Notes

Chapter 1;
Lecture Slides 1
(Background Material = Recommended Reading)
 Chapter 2; Lecture Slides 2 (Linear Systems)

Chapter 3;
Lecture Slides 3
(Least Squares)
 Chapter 4; Lecture Slides 4 (Eigenvalues)
 Chapter 11 (pp.335350); Lecture slides 11 (long) / (short) (Direct and Iterative Methods for Sparse Systems)
Assignments
Assignment  Due date  Solutions  Marks  

Assignment 1  18/02/2019  Solutions 1  Marks 1  
Assignment 2  04/03/2019  Solutions 2  Marks 2  
Assignment 3  13/03/2019  Solutions 3  Marks 3  
Assignment 4  15/04/2019  Solutions 4  Marks 4  
Assignment 5  29/04/2019  Solutions 5  Marks 5  
Assignment 6  13/05/2019  Solutions 6  Marks 6 
Tests
 Test 01 2018 and solutions
 Test 02 2018 and solutions
 Test 01 2019 and solutions
Schedule
Week 1 (Chapter 1) Fundamentals (Undergraduate slides: eng1, eng2 / afr1, afr2)
 Linear systems; Existence and uniqueness of solutions
 Vector and matrix norms
 conditioning of linear systems. (Undergraduate slides: eng / afr)
 Solving linear systems
 Gaussian elimination and LU factorisation
 Pivoting (Proof of PA = LU factorization)
 Algorithmic complexity
 ShermanMorrison formula
 Notes 0109
 Special types of linear systems (Reordering for sparse direct methods)
 Cholesky factorization
 Chapter 3: Least squares
 (Undergraduate notes on least squares: English /Afrikaans)
 Normal equations
 QR Factorization
 Householder transformation
 Givens rotations
 Notes 1016
 Revision
 Test week
 Test week
 Review of eigenvalues, eigenvectors, diagonalization, similarity transforms (Undergraduate slides: eng / afr)
 Power iteration and its variants, Rayleighquotient iteration
 QR iteration
 Some implementation details of QR iteration, Hessenberg factorization
 Arnoldi and Lanczos algorithms
 Notes 1721
 Model problem, sparse matrices. Related undergraduate notes. Notes 22
 Iterative methods for Ax = b: splitting methods; convergence
 Jacobi, GaussSeidel, SOR iterations.
 Jacobi, GaussSeidel, SOR iterations (continued)
 Incomplete LU and Cholesky
 Minimization methods for Ax = b when A is s.p.d.
 Method of steepest descent
 Method of conjugate gradients
 Convergence of CG
 Preconditioned conjugate gradient method.
 MINRES and GMRES
 Rateofconvergence for the 2D Model Problem
 Notes 2329