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|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.|
|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
|Assessment:||Homework, computer labs, and written exam paper at end of semester|
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.|