Aankondigings / Announcements
 Proof of PA = LU factorization mentioned in class availabale here.
 Assignment 02 is available below.
Dosent / Lecturer
First term:
 Dr Nick Hale
 Office: A410
 Email nickhale@sun.ac.za
Second term:
 Prof. JAC Weideman
 Office: A315
 Email weideman@sun.ac.za
Rooster / Timetable
 Monday 11:00 @ M203
 Wednesday 09:00 @ M203
 Thursday 12:00 @ M203
Inligtingstukke / Information Sheets
 Information sheet available here.
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.335350); Lecture slides 11 (long) / (short) (Direct and Iterative Methods for Sparse Systems)
Opdragte / Assignments
 Assignment 1 & Solutions 1 (due Monday 19th Feb)
 Assignment 2 & Solutions 2 (due Thursday 01st March)
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
 Intro to conditioning of linear systems. (Undergraduate slides: eng / afr)
 Solving linear systems
 Elimination
 LU factorization
 Gaussian elimination
 Instability and error growth factor
 Pivoting (Proof of PA = LU factorization)
 Algorithmic complexity
 ShermanMorrison formula
 Special types of linear systems
 Cholesky factorization
 Chapter 3: Least squares
 Normal equations
 Conditioning of LS problem
 QR Factorization
 Householder transformation
 Givens rotations
 GramSchmidt
Test week and Term break
Week 7 (Chapter 4) Review of eigenvalues, eigenvectors, diagonalization (Undergraduate slides: eng / afr)
 Review continued
 Similarity transformations, power iteration and its variants
 Rayleighquotient iteration, QR iteration
 Some implementation details of QR iteration, Hessenberg factorization
 Arnoldi and Lanczos algorithms
 Arnoldi & Lanczos continued
 Model problem, sparse matrices PDE model problem. Related undergraduate notes.
 Direct methods for sparse systems; reordering (classroom demo)
 Iterative methods for Ax = b: splitting methods; convergence
 Jacobi, GaussSeidel, SOR iterations (classroom demo).
 Jacobi, GaussSeidel, SOR iterations (continued)
 Rateofconvergence for the 2D Model Problem
 Minimization methods for Ax = b when A is s.p.d.
 Method of steepest descent (Figure) (Implementation)
 Method of conjugate gradients (Implementation)
 Preconditioned conjugate gradient method. (Clustering Demo) (Convergence of all methods)
MATLAB Kodes / MATLAB Codes
 decode_ieee.m  Decodes an IEEE 754 doubleprecision value.
 cos_demo.m  Demonstrate cancellation error.