TW776/876: Numeriese Metodes/Numerical Methods

TW776/876 (2014)

Numeriese Metodes Numerical Methods

Inligtingstukke Information Sheets

Information Sheet

Aankondigings Announcements

Results: University rules prevent me from posting final scores, but here are the individual scores for assignments and tests.

Assignments: All assignments are available on the table outside A310.

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.
Week 10: Method of steepest descent: derivation.
Week 11: SD continued and intro to CG: summary.
Week 12: Discussion of CG error bounds; pre-conditioning and clustering of eigenvalues; operation counts for the model problem.
Week 13: Derivation of CG error bounds (Kelley Ch. 2; see annotated copy above)

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 14) (solutions)
Assignment 5 (due May 2) (solutions)
Assignment 6 (due May 16) (solutions)

Addisionele Notas Additional Notes

Recommended reading: summary of iterative methods

"How does backslash work?"


JAC Weideman