# CS475/CM375 - Fall 2010  Computational Linear Algebra

Instructor: Pascal Poupart
Office: DC2514
Email: ppoupart [at] cs [dot] uwaterloo [dot] ca
Website: http://www.student.cs.uwaterloo.ca/~cs475
Newsgroup: uw.cs.cs475
Office Hours: Tuesday & Thursday 2:30-4 pm (DC2514)
Lectures: Tuesday & Thursday 10-11:20 am (MC4060)
TA: Lin He (l22he [at] cs [dot] uwaterloo [dot] ca)

## Objectives

Numerical linear algebra is a basic part of many problems in scientific computation. This course provides an overview of algorithms and numerical linear
algebra techniques to solve common problems that arise in many areas such as image processing, search engines, natural language processing, computational finance, aircraft design and artificial intelligence. The course is structured around four
major topics:
1. solving special linear systems,
2. least squares problems,
3. eigenvalue problems, and
4. singular value decomposition.

## Outline

The topics we will cover include:

• Solving Linear Systems:
• LU factorization, Cholesky factorization.
• Special matrices: tridiagonal, band, general sparse matrices.
• Iterative methods, conjugate gradient, convergence.
• Least Squares Problems:
• Pseudo inverse.
• QR factorization.
• Householder transform,
• Givens rotation.
• Eigenvalue Problems:
• Eigenvalues and eigenvectors.
• Characteristic polynomials.
• Schur form.
• Power iteration, inverse iteration.
• QR method.
• Jacobi, divide-and-conquer.
• Singular Value Decomposition:
• Bidiagonalization.
• Search engine.

Prerequisite:

It is assumed that each student has completed an introductory course in numerical computation (i.e., AMATH341, CM271, CS371 or CS370).

Course Organization:

The course material will be covered primarily in lectures. You should also read the appropriate sections of the textbook for each lecture.

There will be four assignments given in the course.  Each assignment will have a theoretical part and a programming part in Matlab. Assignments must be done individually (i.e., no teamwork).  The approximate out and due dates are:

• A1: out Sept 21, due Oct 12
• A2: out Oct 12, due Nov 2
• A3: out Nov 2, due Nov 18
• A4: out Nov 18, due Dec 2
On the due date of an assignment, the work done to date should be submitted at the beginning of class; further material may be submitted for half credit within 24 hours.  Assignments submitted more than 24 hours late will not be marked.

There will be a midterm on Nov 9 and a final exam scheduled by the registrar.

• Assignments (4): 40% (10% each)
• Midterm: 10%
• Final Exam: 50%
In order to pass the course, students must have a pass on the exam component. Thus you must obtain a mark of 30 (out of 60) on the total of the midterm and final exam to pass the course. Otherwise, your final grade will be your exam mark.

## Textbook

Numerical Linear Algebra
L.N. Trefethen and D. Bau III

## Material on Reserve in the library

These reference texts contain the algorithms discussed in class. References to these texts will be made from time to time.

• Numerical Linear Algebra (textbook)
L.N. Trefethen and D. Bau III
QA184.T74, 1997
• Applied Numerical Linear Algebra
J. Demmel
QA184.D455, 1997
• Matrix Computations
G. Golub and C. Van Loan
QA188.G65x, 1989.
• Iterative Methods for Sparse Linear Systems
QA188.S17, 2003. (Also available on-line; see below)
• Direct Methods for Sparse Matrices
Duff, Erisman, Reid
QA188.D84
• Computer Solution of Large Sparse Positive Definite Systems
George and Liu
QA188.G46

## Software and Data

• Netlib
This is a traditional repository for mathematical software. Lots of stuff.
• LAPACK
Linear Algebra PACKage. It is a widely used linear algebra lirary which contains highly efficient implementation of numerical linear algebra methods for solving linear systems, least squares problems, eigenvalue problems, and singular value decomposition.
• Matrix Market contains a set of standard test matrices from fluid dynamics and from engineering.

## Policies

Academic Integrity: In order to maintain a culture of academic integrity, members of the University of Waterloo community are expected to promote honesty, trust, fairness, respect and responsibility. [Check www.uwaterloo.ca/academicintegrity/ for more information.]

Grievance:
A student who believes that a decision affecting some aspect of his/her university life has been unfair or unreasonable may have grounds for initiating a grievance. Read Policy 70, Student Petitions and Grievances, Section 4, www.adm.uwaterloo.ca/infosec/Policies/policy70.htm. When in doubt please be certain to contact the department’s administrative assistant who will provide further assistance.

Discipline:
A student is expected to know what constitutes academic integrity [check www.uwaterloo.ca/academicintegrity/] to avoid committing an academic offence, and to take responsibility for his/her actions. A student who is unsure whether an action constitutes an offence, or who needs help in learning how to avoid offences (e.g., plagiarism, cheating) or about “rules” for group work/collaboration should seek guidance from the course instructor, academic advisor, or the undergraduate Associate Dean. For information on categories of offences and types of penalties, students should refer to Policy 71, Student Discipline, www.adm.uwaterloo.ca/infosec/Policies/policy71.htm. For typical penalties check Guidelines for the Assessment of Penalties, www.adm.uwaterloo.ca/infosec/guidelines/penaltyguidelines.htm.

Appeals: A decision made or penalty imposed under Policy 70 (Student Petitions and Grievances) (other than a petition) or Policy 71 (Student Discipline) may be appealed if there is a
ground. A student who believes he/she has a ground for an appeal should refer to Policy 72 (Student Appeals) www.adm.uwaterloo.ca/infosec/Policies/policy72.htm.

Note for Students with Disabilities: The Office for Persons with Disabilities (OPD), located in Needles Hall, Room 1132, collaborates with all academic departments to arrange appropriate accommodations for students with disabilities without compromising the academic integrity of the curriculum. If you require academic accommodations to lessen the impact of your disability, please register with the OPD at the beginning of each academic term.