STAT 30900/CMSC 37810. Mathematical Computation I —
Department of Statistics
University of Chicago
This is an introductory course on numerical linear algebra. The course
will present a global overview of a number of topics, from classical to
modern to state-of-the-art. The fundamental principles and techniques will
be covered in depth but towards the end of the course we will also discuss
some exciting recent developments.
Numerical linear algebra is quite different from linear algebra. We
will be much less interested in algebraic results that follow from the
axiomatic definitions of fields and vector spaces but much more interested
in analytic results that hold only over the real and complex fields. The
main objects of interest are real- or complex-valued matrices, which may
come from differential operators, integral transforms, bilinear and
quadratic forms, boundary and coboundary maps, Markov chains, graphs,
metrics, correlations, hyperlink structures, cell phone signals, DNA
microarray measurements, movie ratings by viewers, friendship relations in
social networks, etc. Numerical linear algebra provides the mathematical
and algorithmic tools for matrix problems that arise in engineering,
scientific, and statistical applications.
- 11/23/14: Please turn in Homework 5 to Somak in Eckhart 131
during his office hours from 3–5pm on Thu, Dec 4.
- 11/23/14: Lecture notes 10 and Homework 5 posted.
- 11/14/14: Midterm exam 1:30–4:20pm in Eckhart 133.
- 11/09/14: Lecture notes 9 posted.
- 11/06/14: Remarks regarding flop
- 11/05/14: Lecture notes 8 posted.
- 11/03/14: Third make-up lecture tomorrow (Nov 4), 6:00–8:00pm
in Eckhart 133.
- 11/01/14: Lecture notes 7 and Homework 4 posted.
- 10/24/14: Lecture notes 6 and Homework 3 posted.
- 10/21/14: Lecture notes 5 posted.
- 10/20/14: Second make-up lecture tomorrow (Oct 21), 6:00–8:20pm
in Eckhart 133.
- 10/18/14: Lecture notes 4 and Homework 2 posted.
- 10/10/14: Lecture notes 3 and Homework 1 posted.
- 10/08/14: Lecture notes 2 posted.
- 10/06/14: First make-up lecture tomorrow (Oct 7), 6:00–8:00pm in
- 10/05/14: Some of the things I mentioned in class — how
solutions of PDEs and integral equations, Fast Fourier Transforms, Fast
Multipole Methods, etc, can be reduced to matrix computations — have
been superbly described in this set of notes.
- 10/04/14: Lecture notes 1 and Homework 0 posted.
- 10/03/14: We will miss lectures on Nov 14 (midterm exam)
and Nov 28 (Thanksgiving). Make-up
lectures will be held on Tues Oct 7, Oct 21, Nov 4, 6–8pm in
- 10/03/14: Check back regularly for announcements.
Location: Room 133, Eckhart
Times: 1:30–4:20pm on Fri.
Office: Eckhart 122
Tel: (773) 702-4263
Office hours: 2:00–4:00pm on Oct 9 (Thu), Oct 23 (Thu), Nov 6
(Thu), Nov 25 (Tue)
Course Assistant: Somak
Office: Eckhart 8
Office hours: 3:00–5:00pm on Oct 16 (Thu), Oct 30 (Thu), Nov
13 (Thu), Dec 04 (Thu)
The last two topics we would only touch upon briefly (no discussion
of actual algorithms); they would be treated in greater detail in a second
- Linear algebra over R or C: How this course differs
from your undergraduate linear algebra course.
- Three basic matrix decompositions: LU, QR, SVD.
- Gaussian elimination revisited: LU and LDU decompositions.
- Backward error analysis: Guaranteeing correctness in approximate
- Gram–Schmidt orthogonalization revisited: QR and complete
- Solving system of linear equations in the exact and the approximate
sense: Linear systems, least squares, data least squares, total least
- Low rank matrix approximations and matrix completion.
- Iterative methods: Stationary methods and Krylov subspace
- Eigenvalue and singular value problems.
- Sparse linear algebra: Sparse matrices and sparse solutions.
Collaborations are permitted but you
will need to write up your own solutions and declare your collaborators.
The problem sets are designed
to get progressively more difficult. You will get at least six days
for each problem set.
Bug report on the problem sets:
Grade composition: 50% Problem Sets (six altogether, lowest
grade would be dropped), 50% Midterm Exam (Nov 14, 1:30–4:20pm,
in-class, closed book)
We will use the 4th edition of Golub–Van Loan.