TW776/876: Numeriese Metodes/Numerical Methods

TW776/876 (2015)

Numeriese Metodes Numerical Methods

Inligtingstukke Information Sheets

Inligtingstuk; Information Sheet

Aankondigings Announcements

Summary of current marks, now including Test 2 marks: can be found here. Please send Email if you see mistakes. Final marks will be posted via official channels, not here.

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

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)

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

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
Assignment 5 (handed in on April 30) Solutions
Assignment 6 (handed in on May 18) Solutions


nopivotlu.m (GE without pivoting)
Circle fit demo

JAC Weideman