## Course Description

Through the use of lectures, discussions, the text, assignments, and labs, this course will familiarize students with the advanced knowledge of triangular systems, positive definite systems, banded systems, sparse positive definite systems, general systems; Sensitivity of linear systems; orthogonal matrices and least squares; singular value decomposition; eigenvalues and eigenvectors; and QR algorithm with their applications.

See the course outline for more information.

## Course Details

### Lecture Time/Place

Tuesday, 3:15pm–4:05pm; Thursday, 2:15pm–3:05pm; Friday, 4:15pm–5:05pm

All lectures are held in Mulroney Hall, room 3026.

### Textbook

G. H. Golub and C. F. Van Loan, *Matrix Computations*. Johns Hopkins University Press, 4th edition, 2013.

The textbook is not required, but is useful as a secondary reference. Course notes will also be provided for each lecture.

### Marking Scheme

- Two assignments (20% each, total 40%)
- Written report (total 40%): a topic proposal document (10%) and the report itself (30%)
- Brief presentation on the report (10%)
- Participation in lectures (10%)

You must complete both the written report component and the presentation on the report in order to pass the course, even if the weighted sum of your other submissions is at least 50%. You may not complete one without completing the other.

## News

- Mar. 23: Lecture notes for the ninth week have been posted.
- Mar. 17: The second assignment has been posted. It is due by Apr. 5 at 3:15pm.
- Mar. 14: Lecture notes for the eighth week have been posted.
- Mar. 7: Lecture notes for the seventh week have been posted.
- Mar. 1: Information about the report/presentation assessments has been posted.
- Feb. 28: Lecture notes for the sixth week have been posted.
- Feb. 14: Lecture notes for the fifth week have been posted.
- Feb. 7: Lecture notes for the fourth week have been posted.
- Feb. 4: Due to inclement weather, the lecture is cancelled today.
- Jan. 31: Lecture notes for the third week have been posted. The first assignment has also been posted. It is due by Feb. 17 at 2:15pm.
- Jan. 24: Lecture notes for the second week have been posted.
- Jan. 17: Lecture notes for the first week have been posted.
- Jan. 3: Welcome to the course! Please see our Moodle page for details about the course this term.

## Lectures

Week |
Notes |
Readings |

1 | Introduction: matrix multiplication | Golub & Van Loan, 1.1–1.3 |

2 | Review of linear algebra: systems of linear equations | Golub & Van Loan, 2.1, 3.1 |

3 | Gaussian elimination and LU decomposition | Golub & Van Loan, 3.1–3.2 |

4 | Sensitivity and error | Golub & Van Loan, 2.2–2.3, 2.6 |

5 | Least squares: QR decomposition | Golub & Van Loan, 5.1–5.2 |

— | Winter study break | — |

6 | Least squares (cont’d): Gram–Schmidt process | Golub & Van Loan, 5.2–5.3 |

7 | Singular value decomposition | Golub & Van Loan, 2.4, 5.4–5.5 |

8 | Eigenvalues and eigenvectors: power method | Golub & Van Loan, 7.1, 7.3 |

9 | Eigenvalues and eigenvectors (cont’d): QR algorithm | Golub & Van Loan, 7.4–7.5 |

10 | Student presentations | — |

11 | Student presentations | — |

12 | Student presentations | — |

## Code

For some algorithms presented in the lecture notes, an associated Python code file is included below to implement the algorithm. This code is not guaranteed to be the most efficient or most beautiful code, so feel free to modify it, experiment with it, and improve it.

- Week 1: MatVecMult.py, MatMatMult.py, BlockMatMult.py
- Week 2: ForwardSub.py, BackwardSub.py, Cholesky.py
- Week 3: GaussianSolve.py, GaussianLU.py
- Week 4:
*No code* - Week 5: HouseholderQR.py
- Week 6: GramSchmidt.py
- Week 7:
*No code* - Week 8: EigenPower.py

## Assignments

- Assignment 1, due Feb. 17
- Assignment 2, due Apr. 5
- Written Report, due Apr. 14
- Presentation, due date varies

Assignments are due at the beginning of class on the due date. Late assignments will be accepted up to the beginning of the first class following the due date. Late assignments are subject to a penalty of 10% deducted from the earned mark.

The written report and presentation must be submitted on the due date. Late submissions will not be accepted.

## Personnel

### Instructor

Taylor J. Smith

Email: tjsmith [at] stfx [dot] ca

Office: Annex, Room 9A

Student hours: Monday, 9:15am–11:15am