# MA398 Matrix Analysis and Algorithms

**Lecturer:** Radu Cimpeanu

**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 MA259 Multivariable Calculus are sufficient. Helpful but not mandatory is some knowledge of numerical concepts as accuracy, iteration, and stability as provided in MA228 Numerical Analysis or MA261 Differential Equations: Modelling and Numerics.

**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**: 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.

**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.

**Books**:

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.