Lecturer: Stefan Grosskinsky
Term(s): Term 1
Status for Mathematics students: List A
Commitment: 30 lectures
Assessment: Exam (85%) Assignments (15%)
Prerequisites: Core module of the first and second year, in particular MA106 Linear Algebra and MA225 Differentiation, are sufficient. Helpful but not mandatory is some knowledge of numerical concepts as accuracy, iteration, and stability as provided in MA228 Numerical Analysis.
Leads To: A few notions used for the analysis are shared with MA3G7 Functional Analysis I. With respect to implementation and software issues but also towards optimisation problems the module MA4G7 Computational Linear Algebra and Optimization is recommended. A nice application area where various methods provided in this module are needed are numerical methods for partial differential equations, MA3H0 Numerical Analysis and PDEs
Content: Large scale problems in linear algebra as solving systems of linear equations, least-squares problems, and eigenvalue problems lie at the heart of many algorithms in scientific computing and require highly efficient solvers. The module will be based around understanding the mathematical principles underlying the design and the analysis of effective methods and algorithms.
Aims: Understanding how to construct algorithms for solving some problems central in numerical linear algebra and to analyse them with respect to accuracy and computational cost.
Objectives: 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.
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.