Mathematics

Advanced Numerical Analysis (L.6)

Module code: G1110
Level 6
15 credits in autumn semester
Teaching method: Lecture
Assessment modes: Unseen examination, Coursework

This module deepens the second year module Numerical Analysis by providing:

  • analytic insights and computational techniques in iterative methods for linear and nonlinear systems
  • eigenvalue/vector and singular-value problems
  • optimisation and numerical methods for differential equations.

These techniques underpin most modern algorithms of machine learning, data science and scientific computing. The module has both a theoretical and practical component: we learn how to analyse theoretically the algorithms, and gauge their efficiency, alongside their practical coding (in Python or Matlab/Octave) and testing.

Module learning outcomes

  • Analyse the convergence properties of standard iterative methods
  • Implement and apply basic iterative methods to solve linear and nonlinear problems
  • Analyse the convergence and stability properties of standard time-stepping methods
  • Conduct basic error analysis
  • Implement and apply time-stepping methods to solve ODE's and time-dependent PDE's