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.
- 12/02/15: Lecture Notes 17 posted and Lecture Notes 16 updated.
- 12/01/15: Homework 5 posted.
- 11/19/15: Quiz II next Tue, Nov 24, in class.
- 11/19/15: Lecture Notes 16 posted.
- 11/17/15: Lecture Notes 15 posted and Lecture Notes 14 updated.
- 11/12/15: Lecture Notes 14 and Homework 4 posted.
- 11/10/15: Lecture Notes 13 posted.
- 11/06/15: Lecture Notes 12 posted.
- 11/03/15: Lecture Notes 11 and Homework 3 posted.
- 10/27/15: Lecture Notes 10 posted.
- 10/23/15: Lecture Notes 9 posted.
- 10/20/15: Lecture Notes 8 posted.
- 10/19/15: Lecture Notes 7 and Homework 2 posted.
- 10/18/15: Make-up lecture Mon, Oct 19, from 5:30–8:30pm in
- 10/16/15: Lecture Notes 6 posted.
- 10/13/15: Lecture Notes 5 posted.
- 10/12/15: Lecture Notes 4 posted.
- 10/10/15: Marc will give a Matlab tutorial on Fri, Oct
16, 10:30–11:00am in Eckhart 131.
- 10/10/15: Lecture Notes 3 posted.
- 10/07/15: Lecture Notes 2 and Homework 1 posted.
- 10/05/15: Marc will hold office hours this week on Wed, Oct 7,
- 09/29/15: No class on Tue, Oct 6. Make-up lectures on Mon, Oct 12 and
Mon, Oct 19, from 5:30–8:30pm in Eckhart 133.
- 09/29/15: Quiz I on Thu, Oct 29, Quiz II on Tue, Nov 24 (both
- 09/29/15: Lecture Notes 1 and Homework 0 posted.
- 09/29/15: Check back regularly for announcements.
Location: Room 133, Eckhart
Times: 3:00–4:20pm on Tue and Thu.
Office: Eckhart 122
Tel: (773) 702-4263
Office hours: 1:30–3:30pm on Wed.
Course Assistant: Marc
Office: Eckhart 131
Office hours: 11:00am–12:00n on Fri.
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 about 10 days
for each problem set.
Bug report on the problem sets:
Grade composition: 50% Problem Sets (six altogether, lowest
grade would be dropped), 50% Exams (two altogether, in-class, closed book)
Exam dates: Quiz I on Oct 29. Quiz II on Nov 24.
We will use the 4th edition of Golub–Van Loan.