Numerical Linear Algebra

(Winter, 2009)

**Course Objectives:**
Numerical computations are the only realistic way to obtain solutions
of many problems involving large systems of linear equations, eigenvalues of
large matrices, and other problems of linear algebra.
This course focuses on numerical methods and algorithms
for direct and iterative solutions of linear systems, computations
of eigenvalues and eigenvectors, as well as for decompositions, projections, and
factorizations in finite-dimensional vector spaces.
Examples and problems will be implemented in the numerical solution using MATLAB. Theoretical
aspects of matrix norms, condition numbers, computational complexity, stability and
convergence of iterations will be discussed together with practical aspects of
robustness, compactness, and visualizations
of the numerical codes.

**Topics:**
Lectures cover introduction to MATLAB, matrix norms and convergence of algorithms,
solutions of linear systems, least square approximations and orthogonal projections,
and computations of eigenvalues and eigenvectors. Numerical examples and computer assignments are
based on computer programs with Matlab.

**Instructor:**

Dr. Dmitry Pelinovsky, HH-422, ext.23424, e-mail: dmpeli@math.mcmaster.ca

**Teaching Assistant:**

Azzam Hazim, e-mail: hazima@mcmaster.ca

**Hours:**

*Lectures:* Tuesday, Thursday, Friday (11:30-12:20); BSB-108

*Computer Labs:* Wednesday (10:30-11:20); KTH-B121

*Office hours of D.Pelinovsky:* Tuesday, Thursday (10:30-11:20)

*Office hours of A.Hazim:* Thursday (13:30-15:20) in MATHCafe.

**Textbook:**

*"Numerical Mathematics"* by M. Grasselli and D. Pelinovsky
(Jones and Bartlett, 2008), ISBN 9780763737672

**Labs:**
MATLAB 7 is installed in computer lab of KTH.
Lab hours are reserved for the work of students with computer-based problems.
Unless the labs are reserved for large-class tutorials, students might be able to work in the
computer labs beyond the scheduled time. Students are also
encouraged to purchase "The Student Edition of MATLAB"
to be able to work with Matlab at home.

**Assignments:**
Four home assignments will be posted on the course webpage with specific deadlines.
Solutions of the assignments should only include working MATLAB codes and should be
submitted by e-mail to math2t03@math.mcmaster.ca. Results of the three
best assignments will be counted towards the final mark.

**Class Test:**
There will be two class tests on Fridays February 06
and March 20 during the regular lecture hour. The test will
cover analytical questions of the course. Laptops and calculators of all kinds
are allowed on the test.

**Final Exam:** The course is completed by a two-hour final examination.
The date and location of the final exam will be announced by the registrar's office in mid-term.

**Marking scheme:**

Final exam | 40% |

Mid-term tests | 40% |

Assignments | 20% |

**Senate Policy Statement:** The course is regulated under
the following documents:
Statement on Academic Ethics
and Senate Resolutions on Academic Dishonesty. Any student
who infringes one of these resolutions will be treated according
to the published policy. In particular, academic dishonesty includes
(1) plagiarism, e.g. the submission of work that is not one's own,
(2) improper collaboration in group work on home assignments,
(3) copying or using unauthorized aids tests and examinations. It is
your responsibility to understand what constitutes academic dishonesty,
refering to Academic Integrity Policy.

**Additional information:**
Late assignments will not be graded. No make-up tests will be scheduled.
No exemption from one assignment for medical or other reasons is granted.
Exemptions from the test and several assignments for valid reasons are possible,
but must be requested through the office of the Associate Dean of the Faculty
you are registered with. In the event of an exemption, your course grade will be
re-weighted by increasing the weight of the final examination to compensate for
the missed test or assignment.