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.
- 12/03/13: TA's office hour rescheduled to Wed 12–1pm in
- 11/26/13: Homework 5 posted. Please read the footnote for
instructions on turning in your solutions.
- 11/26/13: Lecture notes 16 posted.
- 11/23/13: Lecture notes 15 posted.
- 11/19/13: Today's lecture is cancelled.
- 11/16/13: Lecture notes 13 and 14 posted.
- 11/16/13: Homework 4 posted.
- 11/11/13: Lecture notes 12 posted.
- 11/05/13: Homework 3 and Lecture notes 11 posted.
- 10/26/13: Lecture notes 10 posted.
- 10/24/13: Make-up lectures 5–7pm in Eckhart 133 on Friday Oct
- 10/24/13: Lecture notes 9 posted.
- 10/22/13: Homework 2 and Lecture notes 8 posted.
- 10/17/13: Lecture notes 7 posted.
- 10/16/13: Lecture notes 6 posted.
- 10/14/13: TA is out sick today. Office hours to be rescheduled.
- 10/12/13: If you use Matlab/Scilab/Octave, please make an effort to vectorize your code.
Lecture notes 4 & 5 posted.
- 10/10/13: Homework 1 posted.
- 10/09/13: Matlab tutorial in Eckhart 117, 12–1pm, Fri, Oct
- 10/09/13: Lecture notes 3 posted.
- 10/03/13: Lecture notes 1 & 2 posted.
- 10/02/13: Homework 0 posted.
- 10/01/13: Make-up lectures 5–7pm in Eckhart 133 on Fridays
Oct 11 & Oct 25.
- 10/01/13: As announced in class, lecture notes and other references
are kept in a non-public folder, please write to me for instructions on
- 10/01/13: Check back regularly for announcements.
Location: Room 276, Ryerson
Times: 1:30–2:50pm on Tue/Thu.
Office: Eckhart 122
Tel: (773) 702-4263
Office hours: 2:30–4:00pm, Wed
Course Assistant: Danny Lian
Office: Eckhart 131
Office hours: 2:30–3:30pm, Mon
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.
Except for the take-home final, collaborations are permitted but you
will need to write up your own solutions. The problem sets are designed
to get progressively more difficult. You will get at least seven days
for each problem set.
Bug report on the problem sets:
Grade composition: 50% Problem Sets, 25% Midterm, 25% Final
We will use the 4th edition of Golub-Van Loan.