Lecturer	Andy Wathen
Degrees	2008: Michaelmas Term — MSc in Mathematical Modelling and Scientific Computing
Term	Michaelmas Term 2008  (16 lectures)
Links	Also Part C of MMath degree

Overview

Linear Algebra is a central and widely applicable part of Mathematics. It is estimated that many (if not most) computers in the world are computing with matrix algorithms at any moment in time whether these be embedded in visualization software in a computer game or calculating prices for some financial option. This course builds on elementary linear algebra and in it we derive, describe and analyse a number of widely used constructive methods (algorithms) for various problems involving matrices.

Prerequisites

Only elementary linear algebra is assumed in this course. The part A Numerical Analysis course would be helpful, indeed some swift review and extensions of some of the material of that course is included here.

Synopsis

Numerical Methods for solving linear systems of equations, computing eigenvalues and singular values and various related problems involving matrices are the main focus of this course.

Syllabus

Common problems in linear algebra. Matrix structure, singular value decomposition.

QR factorization, the QR algorithm for eigenvalues.

Direct solution methods for linear systems, Gaussian elimination and its variants.

Iterative solution methods for linear systems.

Chebyshev polynomials and Chebyshev semi-iterative methods, conjugate gradients, convergence analysis, preconditioning.

Reading list

• L N Trefethen and D Bau III, Numerical Linear Algebra, SIAM, 1997

• J W Demmel, Applied Numerial Linear Algebra, SIAM, 1997

• A Greenbaum, Iterative Methods for solving Linear Systems,, SIAM, 1997

• G H Golub and C F van Loan, Matrix Computations, John Hopkins University Press, 3rd edition, 1996

• H C Elman, D J Silvester and A J Wathen, Finite Elements and Fast Iterative Solvers, OUP, 1995 (only chapter 2)

Taking our courses

This form is not to be used by students studying for a degree in the Department of Computer Science, or for Visiting Students who are registered for Computer Science courses

Other matriculated University of Oxford students who are interested in taking this, or other, courses in the Department of Computer Science, must complete this online form by 17.00 on Friday of 0th week of term in which the course is taught. Late requests, and requests sent by email, will not be considered. All requests must be approved by the relevant Computer Science departmental committee and can only be submitted using this form.