Numerical Analysis

Matrix factorizations with applications (direct solvers for linear systems of equations, linear least-squares problems); finite precision arithmetic (IEEE standard, condition of a problem, stability); solution of nonlinear systems of equations (fixed point iteration, Newton's method); interpolation (polynomials, splines); quadrature; additional selected topics: singular value decomposition, fast Fourier transform, eigenvalue problems, Monte Carlo quadrature, sparse matrices

Successful students of this module will understand the algorithmic-numerical way of thinking by means of the basic algorithms from numerical analysis and numerical linear algebra. Students know and can apply the basic techniques for the assessment of the efficiency and accuracy of numerical algorithms, can implement the algorithms with computer programs (using, e.g., MATLAB or Julia), and can apply basic techniques for the estimation of approximation errors.

MA0001 Analysis 1, MA0004 Linear Algebra 1, MA0010 Introduction to Programming

lecture, exercise sessions, assignments and programming for self-study
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.

blackboard, computer experiments

Quarteroni/Sacco/Saleri: Numerical Mathematics, 2nd Edition, Springer, 2007
Ascher/Greif: A First Course in Numerical Methods, SIAM, 2011.
Quarteroni/Saleri/Gervasio: Scientific Computing with MATLAB and Octave, 4th Edition, Springer, 2014.

The module examination is based on a written exam (90 minutes). The algorithmic numerical way of thinking of the students will be assessed together with their ability to implement basic algorithms in a computer program. Students have to show in a limited amount of time that they know and can apply basic techniques for the evaluation of the efficiency and accuracy of numerical algorithms and the estimation of approximation errors.