| TANA50 | Numerical Methods II, ECTS-points /NUMERISKA METODER II/ Advancement level: C | |
| Aim: The student should be able to understand and apply modern techniques for solving important computational problems in Science and Technology. Another purpose is to give knowledge about the use of commercial software for scientific computations. Prerequisites: Numerical Methods I / Numerical Algorithms. A Basic Programming course.Course organization: The course consists of lectures, lessons and computer exercises. Course content: Linear Algebra: Gaussian Elimination. Perturbation Theory. The Singular Value Decomposition and the Pseudoinverse. Orthogonal transformations using the Householder and the Givenīs methods. The QR decomposition and the Least Squares Problem. The Eigenvalue Problem: Invariant subspaces. Normal forms. Perturbation Theory and error estimates. The Rayleigh quotient. The Power method and Inverse Iteration. Transformation to Hessenberg and tridiagonal form. The QR-algorithm. Systems of nonlinear equations: Contractive mappings and fixed point iterations. The Newton Method. Ordinary Differential Equations: The theorem of Picard and Lindelöf. Runge-Kutta methods. Multistep methods. Errror estimates and step lenght control. Difference equations. Stability and Convergence. Methods for stiff systems.Course literature: G. Dahlquist and Åke Björck: Numerical Methods, 2nd ed. (manuscript from the Department of Mathematics) | ||
| TEN1 | , 2 p. | |
| LAB1 | , 0,5 p. | |