NUMERICAL LINEAR ALGEBRA

Winter 2008

Time & Place: 9:30-10:20 on Mondays and Thursdays, 10:30-11:20 on Tuesdays in ABB/271

Computer Labs: 12:30-13:20 on Thursday in BSB/248

Instructor: Dr. Bartosz Protas

Office: HH 326, Ext. 24116

Office hours: 13:30-14:30 on Tuesdays and Thursdays

Teaching Assistant: Masahiro Oishi

Email: oishim_AT_mcmaster_DOT_ca

Office: ITB 115

Office hours: 12:30-13:30 on Tuesdays

Announcements:

- Results and solutions of Homework Assignment #5 are already posted.

- After the end of instruction (April 9), the Teaching Assistant and myself will not be holding our regular office hours; I am available by appointment almost any time until May 7.

- Several review topics are already available; specific questions will be discussed during the review session.

- The review session will take place during 1:30-3:30pm on Tuesday, April 15; venue: HH/104.

Outline of the Course:

The main focus of this course will be on the use of numerical computation to solve problems in linear algebra. Following an introduction to MATLAB, we will discuss relevant properties of the finite-precision arithmetic. Then we will introduce various techniques, both direct and iterative, for efficient solution of systems of linear equation. We will also study numerical computation of eigenvalues and eigenvectors, as well as some other useful decompositions and factorizations. In addition to discussing theoretical aspects such as conditioning, computational complexity and convergence, for every problem we will also present an implementation of the actual solution method using MATLAB. As a motivation, we will be using examples taken from various areas of numerical mathematics complemented with some ideas from abstract algebra.**Topics:**

Dates |
Topics |
Chapters from the textbook |

Jan 7 - Jan 24 |
introduction, MATLAB, finite-precision arithmetic |
1 |

Jan 28 - Feb 28 |
review of linear algebra, linear systems, direct and iterative solution methods |
2 |

Mar 3 - Mar 20 |
orthogonal projections, QR factorizations |
3 |

Mar 24 - Apr 8 |
eigenvalues and eigenvectors, singular value decomposition |
4 |

Course Objectives:

By the end of the course students should be able to develop MATLAB codes for the numerical solution of some standard problems in linear algebra.Primary Reference:

Supplemental Reference:

Software:

All of the computational examples will be presented using MATLAB. This software is available on the computers in the computer lab. Lab hours (see above) are reserved for unsupervised work with computer-based assignments. Unless they are reserved for large-class tutorials, students should be able to work in the computer labs in BSB also outside the allocated time-slots. Students are as well encouraged to purchasePrerequisites:

Linear Algebra II (MATH2R03)Assignments:

Five homework assignments will be posted on the course website on the dates indicated in the table below. The assignments will be due by midnight on Tuesday the following week. Solutions of the assignments should be submitted by e-mail to math2t03_AT_math_DOT_mcmaster_DOT_ca using the template provided. Late submissions will not be accepted. Only four best assignments are counted towards the final mark. The assignments and solutions will be posted on the course webpage.**Homework Post & Due Dates:**

# |
Post Date |
Due Date |

HW 1 |
January 22 |
January 29 |

HW 2 |
February 5 |
February 12 |

HW 3 |
February 26 |
March 4 |

HW 4 |
March 18 |
March 25 |

HW 5 |
April 1 |
April 8 |

Class Quizzes:

There will be two in-class quizzes on February 5 and March 18 in T29-101. They will last 50 minutes and will cover analytical issues only (no programming). Only the McMaster standard calculator Casio fx-991 will be allowed during the quizzes.Final Exam:

The course will be completed by a three-hour final examination. The date and location of the final exam will be announced by the Registrar's office in mid-term.Marking Scheme:

Excused Absences:

Exemptions from the assignments or tests for valid reasons are possible, but must be requested through the office of the Associate Dean of the Faculty that you are registered with. In the event of an exemption, no make up test or assignment will be administered, but your course grade will be re-weighted by increasing the weight of the final examination to compensate for the missed test or assignment.Academic Integrity:

You are expected to exhibit honesty and use ethical behaviour in all aspects of the learning process. Academic credentials you earn are rooted in principles of honesty and academic integrity.Academic dishonesty is to knowingly act or fail to act in a way that results or could result in unearned academic credit or advantage. This behaviour can result in serious consequences, e.g., the grade of zero on an assignment, loss of credit with a notation on the transcript (notation reads: "Grade of F assigned for academic dishonesty"), and/or suspension or expulsion from the university.

It is your responsibility to understand what constitutes academic dishonesty. For information on the various types of academic dishonesty please refer to the

Important Notice:

The instructor reserves the right to modify elements of the course and will notify students accordingly (in class and post any changes to the course website).