| Lecturer: |
Dr Niall Madden
|
|
| Lectures: |
24 x 1 hour lectures in Semester 2, plus
labs and tutorials.
|
| Schedule: |
Lectures are on Monday 9-10 and Thursday 11-12 in
C219 (Aras de Brun). The first class will be on 11th of Jan,
2010. Labs take place (for now) Wed 11-12, Civil Eng lab.
|
| Credits: |
9 ECTS
|
| Content: |
The construction and
analysis of direct and iterative methods for the solution of
linear systems of equations, and the estimation of
eigenvalues and eigenvectors.
Starting fundamental ideas of orthogonality, norms and the Singular
Value Decomposition, we introduce QR
factorisation, and the notion of the condition number of a
matrix.
We then look at the direct solution of linear systems using
Gaussian Elimination, and its variants (e.g., Cholesky
Factorisation, Thomas Algorithm).
This is followed by a study of some iterative techniques (e.g,
conjugate gradients, Krylov Sequence Methods) for
solving linear systems, and estimating eigenvalues and
eigenvectors.
|
| What you will learn: |
How to select an appropriate algorithm for a given
linear algebra problem, show (mathematically) that it will
work, and implemented it on a computer (usually using
Matlab).
|
| Why take this course: |
The solution to many problems in pure and applied
mathematics -- from graphics in computer games, to
retrieving information from the Internet -- require
algorithms for solving linear systems or estimating
eigenvalues/vectors. But often it is not possible to treat
these methods as "black boxes": we have to understand them
in order to be able to use them correctly.
For a few interesting articles on applications of methods that will
be introduced in this course (and that might lead to a
dissertation topic) see
- Professor SVD, by Cleve Moler.
- Singular Value Decomposition, Eigenfaces, and 3D Reconstructions by Neil Muller, Lourenco Magaia, B.M. Herbst
- How Google Finds Your Needle in the Web's Haystack
by David Austin.
- The
$25,000,000,000 Eigenvector: The Linear
Algebra Behind Google" by Kurt Bryan and
Tanya Leise.
-
A Survey of Eigenvector Methods for Web Information Retrieval by
Amy N. Langville, Carl D. Meyer in SIAM
Review Volume 47, Number 1.
|
| Assessment: |
Homework, computer labs, and written exam paper at
end of semester |
| Texts: |
Trefethen and Bau, Numerical
Linear Algebra. (512.5 TRE). I
strongly recommend you buy a copy of this book.
GW Stewart, Afternotes goes to graduate school (519.4 STE)
JW Demmel,
Applied numerical linear algebra (512.5 DEM)
Horn and Johnson,
Matrix Analysis (512.8)
Harry Dym,
Linear Algebra in Action (512.5 DYM)
C Moler, Numerical Computing with MATLAB
(518.0285 MOL).
DJ Higham and NJ Higham MATLAB
Guide (518.0285 HIG)
(518.0285 MOL).
|
| Prerequisites:
| A solid grounding in linear algebra. For NUI
Galway applicants, MA283, MA313/314 or MA250 would suffice.
|
|
Leagan Gaeilge
Text Version
Printer Friendly
Sitemap
