Test 2 and Assignment 8 have been marked, a summary of all marks
can be found here
Please send Email if there are mistakes.
Assignment 8 Solutions
Assignment 7 has been marked and is available on the desk outside A310 (Applied Math).
Assignment 8 will be placed in the same place as soon as it is marked.
May 1 material: In case you have not yet watched the MIT video lectures, they can be found right at the bottom of this page.
Further reading on CG: The conjugate gradient method without the agonizing pain
This year, we shall try as an experiment the text book
G Allaire, SM Kaber, Numerical Linear Algebra, Springer, 2008
which is available for short term loan at the
front desk of the Engineering Library.
In addition, the following items are also put on Reserve.
Barret et al: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd Edition, SIAM 1994
JW Demmel: Applied Numerical Linear Algebra, SIAM 1997
Y Saad: Iterative Methods for Sparse Linear Systems, SIAM 2003
(The online version of Saad's book is available here. To save bandwidth, a local copy is kept here.)
LN Trefethen, D Bau: Numerical Linear Algebra, SIAM 1997
Week 1: Model problems (A&K Ch 1: Sections 1.1, 1.2 covered in class; 1.3, 1.4, 1.5 for self study)
Week 2: Matrix background (A&K, Ch 2: we shall skip 2.1, 2.2.5, 2.6 for now)
Week 3: SVD (2.7), Matrix norms (3.1; leave 3.3 for later)
Week 4: Linear systems (Ch 5: only 5.3.2, 5.3.3)
Week 5: Direct methods for linear systems (Ch 6: 6.1, 6.2)
Week 6: Direct methods for linear systems continued (6.3, 6.4)
Week 7: Householder (7.3.4; only square matrices)
Week 8: Test 1, Wednesday, March 27, 14:00-16:00
Vacation 29/3-7/4 (no classes)
Week 9: 2D Model Problem; simple iterative methods (8.1)
Week 10: Jacobi, Gauss-Seidel, SOR (8.2); incomplete LU/Cholesky
Week 11: Richardson, steepest descent, and introduction to conjugate gradients (9.1, 9.2, 9.3, 9.4)
Week 12: Reading plus video lectures (see below); conjugate gradients (9.5)
Week 13: Pre-conditioned CG (9.5), Lanczos method (10.7)
Week 14: Test 2, Friday, May 17, 11:00-13:00
Test 1 (with solutions)
Assignment 1 Solutions
Assignment 2 Solutions
Assignment 3 Solutions
Assignment 4 Solutions
Assignment 5 Solutions
Assignment 6 Solutions
The marker for your assignment sets is PhD student in Applied Math, Eyaya Eneyew.
If there is something substantial you feel you need to discuss with him, you can send him Email to set up an appointment.
His address is his first name at sun. Please do not bother him over small issues.
Summary of spectral factorizations (Handout Feb 20)
Geometry of a Householder reflection (Handout March 20)
All chapters, umarked
Here is the MIT lecture (90MB) on reordering, as mentioned in class on April 10.
There was a request for additional help with MATLAB. A very popular and well written text is
TA Driscoll, Learning MATLAB, SIAM, 2009
Unfortunately the SU Library System does not seem to have a copy. Alternatively, the following books can be consulted. They will be placed for short term loan at the Engineering Library.
SJ Chapman, Essentials of MATLAB programming, Cengage, 2009
BD Hahn, Essential MATLAB for scientists and engineers, Elsevier, 2002
DJ Higham, MATLAB Guide, SIAM, 2000
May 1: We have lost a double lecture hour on Wednesday, May 1, because of the vacation day.
Here are the plans for catching up.
The following material comes from MIT OpenCourseWare ; specifically graduate course 18.086 Mathematical Methods for Engineers II.
Reading: The following are draft sections from the book Computational Science and Engineering, Wellesley-Cambridge Press, by Professor Gilbert Strang (full text on reserve at the library). Iterative Methods, Multigrid (optional but recommended), Krylov Subspaces and Conjugate Gradients
Video Lectures: These are big files. It is recommended that you watch them
locally, on the US network. The two lectures on multigrid are optional, but
Iterative Methods, Multigrid I, Multigrid II, Krylov and CG
(If necessary, you can download the VLC 2.0 player here)
JAC Weideman Last modified: Thu Feb 23 13:06:44 GMT 2012