Aankondigings / Announcements
Test 01 on Tuesday 14 March @ 8AM (Venue TBC).
ASSIGNMENT 02 CORRECTIONS
- For Problem 3(c) rather change the a 3,3 entry to 6.
- Problem 4 is optional.
Dosent / Lecturer
- Dr Nick Hale
- Office: A410
- Email email@example.com
- Prof. JAC Weideman
- Office: A315
- Email firstname.lastname@example.org
Rooster / Timetable
- Tuesday 13:00 @ M203
- Wednesday 10:00 @ M203
- Thursday 10:00 @ M203
Inligtingstukke / Information SheetsInformation Sheet
Notas / NotesMATLAB Intro and accompanying lecture slides Afrikaans / English
Opdragte / Assignments
2017 Skedule / Schedule (tentative)
Week 1 (Jan 31, Feb 1,2):
- 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)
Week 2 (Feb 7,8,9):
- Solving linear systems
- LU factorization
- Gaussian elimination
Week 3 (Feb 14,15,16):
- Instability and error growth factor
- Algorithmic complexity
- Sherman-Morrison formula
Week 4 (Feb 21,22,23):
- Special types of linear systems
- Cholesky factorization
- Chapter 3: Least squares
- Normal equations
Week 5 (Feb 28, Mar 1,2):
- Conditioning of LS problem
- QR Factorization
- Householder transformation
- Givens rotations
Week 6 (Mar 7,8,9):
- Singular value decomposition (SVD)
MATLAB Kodes / MATLAB Codes
- decode_ieee.m - Decodes an IEEE 754 double-precision value.
- cos_demo.m - Demonstrate cancellation error.
2016 Skedule / Schedule (for reference)
Week 2 (Feb 9&11): Conditioning (cont); the A = LU and PA = LU factorizations.
Week 3 (Feb 16&18): Instability of GE and the growth factor; Complexity of matrix computations; Sherman-Morrison formula
Week 5 (Mar 1&3): Least squares problem (cont); Orthogonal matrices; QR factorization with Gram-Schmidt.
Test week & Easter break
Week 7 (Mar 29&31): Eigenvalues: intro, similarity, power iterations, Rayleigh-Quotient iteration. Properties of symmetric/Hermitian matrices
Week 8 (Apr 5&7): QR iteration. Lanczos & Arnoldi algorithms.
Week 10 (Apr 19&21): Jacobi, Gauss-Seidel, SOR, Incomplete Cholesky iterations. Convergence rates and complexity for the 2D model problem.
Week 11 (Apr 26&28): Convergence rates and complexity (cont). Quadratic forms. Solving s.p.d. systems with minimization methods. Method of steepest descents.
Week 12 (May 3; no class on May 5): Conjugate gradient method (CG).
Week 13 (May 10 & 12): Preconditioned CG method. Error estimates for CG. Nonsymmetric variants of CG.