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