CMSC37800/STAT30700 Numerical Computation

This is a graduate course in numerical linear algebra, assuming familiarity with undergraduate linear algebra and basic programming skills. We will be studying fundamental ideas such as the singular value decomposition, factorizations for least squares and linear systenms, eigenvalues, and iterative methods.

Class information

InstructorRobert Kirby (
TimeMWF 11:30-12:20
PlaceRyerson 277 (in the annex)
Office hoursMWF 10:30-11:20//Ryerson 259


There will be weekly homework assignments, plus a midterm and a final exam. Each will be weighted as a third of the grade.


Our main text is "Numerical Linear Algebra" by Trefethen and Bau (SIAM press). You may order it online from SIAM or SIAM gives notoriously bad deals to university book stores, so it is not available on campus.

Another good book is "Applied Numerical Linear Algebra" by Demmel, also from SIAM press

An encyclopedic reference is "Matrix Computations" by Golub & van Loan.


26 Sept 05 Class information, Matrices, vectors, inner products, and orthogonality
28 Sept 05Orthogonality and norms
30 Sept 05The singular value decomposition
3 Oct 05More on the SVD
5 Oct 05Projections
7 Oct 05The QR factorization & Gram Schmidt
10 Oct 05Householder triangularization
12 Oct 05Least squares problems
14 Oct 05Conditioning of mathematical problems
17 Oct 05Floating point arithmetic, stability
19 Oct 05More on stability
21 Oct 05Stability, cont'd
24 Oct 05Conditioning of least squares
26 Oct 05Stability for least squares
28 Oct 05Rank-deficient least squares
31 Oct 05LU factorization
2 Nov 05Stability of LU factorization and pivoting
4 Nov 05Midterm
7 Nov 05Eigenvalue problems
9 Nov 05Basic pieces of eigenvalue solvers
11 Nov 05Iteration schemes
14 Nov 05QR Algorithm and shifting
16 Nov 05Computing the SVD
18 Nov 05Introducing iterative methods
21 Nov 05Arnoldi iteration
23 Nov 05No class
25 Nov 05No class
28 Nov 05GMRES
30 Nov 05Conjugate Gradients
2 Dec 05Preconditioning


Problem numbers refer to Exercises in Trefethen and Bau.

Due DateProblems
3 Oct 20051.1,1.2,2.5,2.6,3.2,3.6,4.1,4.3,4.4
10 Oct 20055.2,5.4,6.1,6.2,6.3,6.5,7.2,7.4,7.5
17 Oct 20058.2,8.3,10.1,10.2,10.3,11.1,11.2,12.2,12.3
24 Oct 200513.2,13.3,14.1,15.1,16.2,17.2
31 Oct 200518.1,18.4,19.1,20.1
14 Nov 200520.2,20.3,21.2,21.6,24.2,25.2,26.3
21 Nov 200527.3,27.4,28.2,29.1
2 Dec 200531.3,33.2,35.4,38.3

Final exam

Work the following problems from Trefethen and Bau. You may use the textbook, Demmel, Golub and van Loan, or course notes. You may not refer to material found on the Internet. You may use MATLAB/Octave. You may not consult with any other person or people while working the exam. 9.2, 10.4, 16.1, 25.3, 27.1, 35.6. Solutions are due Monday, December 5, 2005 at noon, at the instructor's office.

Robert Kirby
Last modified: Fri Sep 23 09:57:35 CDT 2005