Announcements

Due date for Assignment 3 postponed to April 22. Problems 4(b) and 8(b) have been dropped. (You can still submit them for a few bonus marks.)

New video to accompany Week 7 self-study: here

If you have questions on any Assignment, please send email. I will share my response with everyone. This will be done anonymously (that is, even if you think your question is trivial nobody will know :-)

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.)
• Strongly recommended: complete the (free) online MATLAB Onramp as a refresher.

Lecturer

• Prof JAC Weideman, Office: A315, Email: weideman@sun.ac.za

Timetable

Tuesday 11:00 and 12:00; Wednesday 12:00

Information Sheets

• Information sheet available here.

Notes

• Chapter 1; Lecture Slides 1 (Undergraduate slides: eng1, eng2 / afr1, afr2) (Background Material) <- Read!
  
• Chapter 2; Lecture Slides 2 (Linear Systems)
• Chapter 3; Lecture Slides 3 (Least Squares)
  
• Chapter 4; Lecture Slides 4 (Eigenvalues)
• Chapter 11 (pp.335-350); Lecture slides 11 (long) / (short) (Direct and Iterative Methods for Sparse Systems)

Assignments

Assignment	Date out	Date in	Solutions
Assignment 1	11/02/2020	25/02/2020	Solutions 1
Assignment 2	25/02/2020	11/03/2020	Solutions 2
Assignment 3	11/03/2020	22/04/2020	Solutions 3
Assignment 4			Solutions 4
Assignment 5			Solutions 5
Assignment 6			Solutions 6

Tests

Test 1: Tuesday April 7, 11:00-13:00, A308 (closed book, closed notes) Postponed

Test 1 will cover the material of Weeks 1-6 in the SCHEDULE box below.

Excluded material:

• Lecture slides chapter 2: pages 24, 28, 64, 70, 73-74, 84-85, 91, 96-100
• Lecture slides chapter 3: pages 18, 24-25, 54-66

Suggestions for preparation:

• Study lecture slides and additional whiteboard notes
• Study the text book and solve the exercises at the end of each chapter
• Read further on each topic by consulting Wikipedia, MathWorld and other reputable Web resources
• Work the practice exams below

• Test 1 2015 (no solutions given, collaborate with your class mates)
• Test 1 2019 and solutions
• Test 2 2019 and solutions

Schedule

Week 1 (Chapter 2)

• Linear systems; Existence and uniqueness of solutions
• Vector and matrix norms

Week 2 (Chapter 2)

• Condition numbers. (Classroom demo of 11 Feb here)
• Conditioning of linear systems. (Undergraduate slides: eng / afr)
• Solving linear systems

Week 3 (Chapter 2)

• Gaussian elimination and LU factorisation (Classroom demo of 18 Feb here)
• Pivoting
• Stability of GE and the growth factor

Week 4 (Chapter 2)

• Complexity (operation count) of LU factorization and triangular solves
• Symmetric positive definite matrices and Cholesky factorization
• Band matrices and sparse matrices
• Condition number estimation

Week 5 (Chapter 3)

• Overdetermined systems and the method of least squares (Undergraduate slides: eng / afr)
• Derivation of the normal equations by differentiation and by geometry
• QR factorization

Week 6 (Chapter 3)

• QR factorization by the Gram-Schmidt and modified Gram-Schmidt procedures.
• Householder reflectors (additional note)
• Givens rotations

Week 7 (Chapter 4) Self-study summary here

• Revision of eigenvalues/vectors and the eigenvalue decomposition
• Special properties of eigenvalues/vectors for symmetric matrices; application to quadratic curves
• Instability of the characteristic polynomial in f-p arithmetic, companion matrices