Lecturer	Nick Trefethen
Term	Michaelmas Term 2008  (12 lectures)

Overview

This course is only offered every other year.
We will run it again in 2010/11.

A MATLAB-based course for graduate students in the Mathematical, Physical and Life Sciences Division.
Part II of this course runs in Hilary Term 2009.

There is a flier with summary information.

Syllabus

TERM 1 - MT 2008 - OUTLINE OF LECTURES

  I. SPARSE MATRICES AND ITERATIVE METHODS

     I.1   View of the field
     I.2   How fast can we solve Ax=b ?
     I.3   Sparse matrices
     I.4   Conjugate gradients
     I.5   Convergence of CG
     I.6   Preconditioned CG
     I.7   Examples of preconditioners
     I.8   The definition of numerical analysis
     I.9   Overview of matrix iterations
     I.10  Lanczos iteration
     I.11  Numerical software tools and information sources

 II. DENSE LINEAR ALGEBRA

    II.1   Matrices, vectors and expansions
    II.2   Orthogonal vectors and matrices
    II.3   QR factorisation
    II.4   Computation of the QR factorisation
    II.5   Linear least-squares
    II.6   Floating point arithmetic
    II.7   Backward error analysis
    II.8   Matrix factorisations
    II.9   SVD

III. OPTIMIZATION

   III.1   Newton's method for a single equation
   III.2   Newton's method for a system of equations
   III.3   Newton's method for minimising a function of 1 variable
   III.4   Newton's method for min. a fun. of several variables
   III.5   From Newton's method to practical optimization
   III.6   Constraints and linear programming
   III.7   NEOS

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.