** Summary of current marks: ** can be found
here.
Please send Email if you see mistakes.

** Assignment 6: ** has been marked and can be picked up
outside A310

** Test 2: ** Date: Tuesday May 26 at 14:00.
Covers material of Weeks 8-14 (as summarized below).
Sample Test

** Reading for CG:** Additional
notes;
Original 1952
paper
by Hestenes & Stiefel

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 (pp.39-89) (Iterative Methods)

** Week 1** (Feb 4&5):
Linear systems; existence and uniqueness of solutions;
vector and matrix norms;
intro to conditioning of linear systems.

** Week 2** (Feb 11&12):
Conditioning (cont); the A = LU and PA = LU factorizations.
Undergraduate notes on conditioning
English
Afrikaans

** Week 3** (Feb 18&19):
Instability of GE and the growth factor; Complexity of matrix computations; Sherman-Morrison formula

** Week 4** (Feb 25&26):
Symmetric positive definite systems; Cholesky factorization;
Review of the least squares problem; Normal equations.
Undergraduate notes on least squares
English
Afrikaans

** Week 5** (Mar 4&5):
Least squares problem (cont), QR factorization with Gram-Schmidt.

** Week 6** (Mar 11&12):
Least squares problem (cont), Solving LS problem with Householder
notes

** Week 7** (Mar 18&19):
Least squares problem (cont), Givens rotations
schematic shown in class;
Revision of the eigenvalue problem

** Week 8** (Mar 25&26):
Eigenvalues: power iterations, Rayleigh-Quotient
iteration, QR iteration
QR classroom demo

** Week 9** (Apr 1&2):
No class because of Eng Test week

** Week 10** (Apr 15&16):
Lanczos & Arnoldi iterations;
Arnoldi handout;
PDE model problem

** Week 11** (Apr 22&23): Direct methods for sparse Ax=b: fill-in and reordering.
Iterative methods for sparse Ax = b: stationary iterations (Jacobi, Gauss-Seidel, SOR, incomplete LU)

** Week 12** (Apr 29): Incomplete LU/Cholesky, Minimization
methods for the Model Problem (Steepest Descent, Conjugate Gradient)

** Week 13** (May 6&7): Conjugate Gradient, Preconditioned
Conjugate Gradient

** Week 14** (May 13&14): SSOR; Rate of convergence for the 2D
model problem; Convergence of CG

Assignment 1 (handed in on Feb 19)
Solutions

Assignment 2 (handed in on March 5)
Solutions

Assignment 3 (handed in on March 19)
Solutions

Assignment 4 (handed in on April 16)
Solutions

Assignment 5 (handed in on April 30)
Solutions

Assignment 6 (handed in on May 18)
(solutions to be posted)

nopivotlu.m (GE without pivoting)

Circle fit demo

JAC Weideman