TW776/876: Numeriese Metodes/Numerical Methods
##
TW776/876 (2015)

## Numeriese Metodes
Numerical Methods

### Inligtingstukke Information Sheets

Inligtingstuk;
Information Sheet

### Aankondigings Announcements

** Fifth assignment ** (due 2015/04/30):
Assignment 5
Since there is no lecture on the due date (Friday schedule)
you can (a) hand in the day before at the Wednesday lecture, or (b)
a folder will be placed outside room A310 where it
can be handed in before the due date and time that appears
on the assignment sheet

** Test 2 date: ** Tuesday May 26 at 14:00 (tentative)

### Notas Notes

Chapter 1;
Lecture Slides 1
(Background Material = Recommended Reading)
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)

### Skedule Schedule

** 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)

### Opdragte Assignments

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

### MATLAB Kodes
MATLAB Codes

nopivotlu.m (GE without pivoting)

Circle fit demo

JAC Weideman