TW776/876: Numeriese Metodes/Numerical Methods

TW776/876 (2014)

Numeriese Metodes Numerical Methods

Inligtingstukke Information Sheets

Information Sheet

Aankondigings Announcements

Second Test: Wednesday May 28, 9:00-11:00

Test 1: Solutions

Equipment Failure: Apologies for the equipment failure on Tuesday March 18. Here is the link that I wanted to display in connection to the question "How does backslash work?"

Handboeke Text Books

ICF Ipsen, Numerical Matrix Analysis SIAM, 2009 (author page)
CT Kelley, Iterative Methods for Linear and Nonlinear Equations , SIAM, 1995 (author page)

Skedule Schedule

Week 1: Ipsen, Chapter 1
Week 2: Ipsen, Sections 2.1-2.6 plus conditioning of Ax=b (corrected) and Hilbert matrix demo
Week 3: Case study: Ill-conditioning of Vandermonde (code); Ipsen 2.7 (read only), 2.8 (pay attention to Fact 2.25, Def 2.27, Cor 2.30), 3.1, 3.2 (skim Facts 3.8, 3.9 and Cor 3.10), 3.3
Week 4: 3.4 (statements of Facts 3.14+3.17 are important, not proofs), 3.5 (simpler version of Alg 3.3 discussed in class is good enough), 3.6 (Def 3.23+Facts 3.24-3.26)
Week 5: 3.6, 3.7 plus Gram-Schmidt and Householder
Week 6: Efficient computation with Housholder reflections; (Test 2 starts here ->) undergraduate review of method of least squares
Week 7: Solving the least squares problem with QR (last page and a bit of 5.3)

Vacation Break

Week 8: Review of eigenvalues and diagonalization; eigenvalues, norms and condition numbers of spd matrices.
Week 9: 1D and 2D model problems; Prof Strang lecture (local copy) (external copy); iterative methods.

Opdragte & Toetse Assignments & Tests

Assignment 1 (due Feb 17) (solutions)
Assignment 2 (due March 3) (solutions)
Assignment 3 (due March 17) (solutions)
Assignment 4 (due April 7) (extended to April 14)
Assignment 5 (due April 29)

Klasnotas Class Notes


JAC Weideman