STAT 30900/CMSC 37810. Mathematical Computation I — Matrix Computation

Department of Statistics
University of Chicago
Fall 2013

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.

Announcements

12/03/13: TA's office hour rescheduled to Wed 12–1pm in Eckhart 131.
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 25.
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.
10/12/13: Lecture notes 4 & 5 posted.
10/10/13: Homework 1 posted.
10/09/13: Matlab tutorial in Eckhart 117, 12–1pm, Fri, Oct 9.
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 accessing them.
10/01/13: Check back regularly for announcements.

Lectures

Location: Room 276, Ryerson Physical Laboratory.

Times: 1:30–2:50pm on Tue/Thu.

Course staff

Instructor: Lek-Heng Lim
Office: Eckhart 122
lekheng(at)galton.uchicago.edu
Tel: (773) 702-4263
Office hours: 2:30–4:00pm, Wed

Course Assistant: Danny Lian Huan Ng
Office: Eckhart 131
lianhuanng(at)uchicago.edu
Office hours: 2:30–3:30pm, Mon

Syllabus

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 course.

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 computations.

Gram-Schmidt orthogonalization revisited: QR and complete orthogonal decompositions.

Solving system of linear equations in the exact and the approximate sense: Linear systems, least squares, data least squares, total least squares.

Low rank matrix approximations and matrix completion.

Iterative methods: Stationary methods and Krylov subspace methods.

Eigenvalue and singular value problems.

Sparse linear algebra: Sparse matrices and sparse solutions.

Problem Sets

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.