Master's Programme in Mathematics and Statistics is responsible for the course.
The course belongs to the Mathematics and Applied mathematics module.
The course is available to students from other degree programmes.
The main skills that the students shall develop are:
- the ability to go from the continuous setting to the discrete one being aware of stability and conditioning issues;
- the ability to use the tools of discrete mathematics for the implementation of effective and efficient algorithms;
- the ability to visualise and analyze the result obtained by using interactive environments.
Recommended time/stage of studies for completion: 1. or 2. year
Prerequisites: Linear algebra and Calculus.
Recommended optional studies: Bachelor studies.
Term/teaching period when the course will be offered: varying.
Computer arithmetic: round-off errors, conditioning of a problem and stability of an algorithm, error propagation.
Systems of linear equations: direct methods (LU, Choleski and QR decompositions), iterative methods and methods for sparse matrices. Conditioning and perturbation theory.
Data approximation with least squares method.
Interpolation and polynomial approximation: Lagrange, Newton and Hermite polynomials. Interpolation error. Runge phenomenon.
Numerical integration (quadrature): Newton-Cotes and composite formulas.
Systems of non-linear equations.
Final report of the project work.
Burden R. L., Faires J.D., Numerical Analysis, Prindle Weber & Schmidt, Boston MA. 2004
Quarteroni A., Sacco R., Saleri F., Numerical Mathematics, Springer-Verlag Berlin Heidelberg, 2007
Exercises and project work. The course will be graded with grades 1-5.