Mathematics
Advanced Numerical Analysis (L.6)
Module code: G1110
Level 6
15 credits in autumn semester
Teaching method: Lecture
Assessment modes: Coursework, Unseen examination
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