Introductory description

Many large scale problems arising in data analysis and scientific computing require to solve systems of linear equations, least-squares problems, and eigenvalue problems, for which highly efficient solvers are required. The module will be based around understanding the mathematical principles underlying the design and the analysis of effective methods and algorithms.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Many large scale problems arising in data analysis and scientific computing require efficient solutions to systems of linear equations, least-squares problems, and eigenvalue problems. The module is based around understanding the mathematical principles underlying the design and the analysis of effective methods and algorithms to solve these types of challenges. Key concepts include matrix decompositions, factorisations and iterative solvers. They are supported by fundamental aspects related to floating point arithmetic, computational cost analysis, stability and convergence.

Learning outcomes

By the end of the module, students should be able to:

• At the end of the module you will familiar with concepts and ideas related to: various matrix factorisations as the theoretical basis for algorithms,
• assessing algorithms with respect to computational cost,
• conditioning of problems and stability of algorithms,
• direct versus iterative methods.

Indicative reading list

AM Stuart and J Voss, Matrix Analysis and Algorithms, script.
G Golub and C van Loan, Matrix Computations, 3. ed., Johns Hopkins Univ. Press, London 1996.
NJ Higham, Accuracy and Stability of Numerical Algorithms, SIAM 1996.
RA Horn and CR Johnson, Matrix Analysis, Cambridge University Press 1985.
D Kincaid and W Cheney, Numerical Analysis, 3. ed., AMS 2002.
LN Trefethen and D Bau, Numerical Linear Algebra, SIAM 1997.

Subject specific skills

Discrete mathematical analysis, algorithmic construction, cost analysis, concepts in numerical methods for applied problems.

Transferable skills

Informed problem solving, software development, creative solution analysis, project management, critical thinking, application-oriented solution strategy design, programming language expertise.