| About Mastermath |
| Courses & exams |
| Program & schedule |
| Registration & Evaluation |
| Links |
| Locations |
| Contact |
|
Numerical Linear Algebra
| Credits | 8 credit points |
| Instructors | Sleijpen, G.L.G. (Universiteit Utrecht), Gijzen, M.B. van (Technische Universiteit Delft) |
| G.L.G.Sleijpen@math.uu.nl, M.B.vanGijzen@tudelft.nl | |
| Aim | To provide theoretical insight and to develop practical skills for solving numerically large scale linear algebra problems. Particular emphasis lies on large-scale linear systems and on eigenvalue problems. |
| Description | Large sparse linear systems or eigenvalue problems arise in many applications, such as weather forecasting, airplane design, tomographic problems, analysis of the stability of structures etc. The solution of these problems is normally the most time-consuming part of the whole calculation. Therefore, the development of new solution algorithms is still an important and very active area of research. The course will give an overview of the modern solution algorithms for linear systems and eigenvalues problems. The course will start with a review of basic concepts from linear algebra, after which the direct solution methods (LU, QR and Choleski decomposition) will be discussed. Next, the basic ideas for iterative solution methods will be explained, which will lead to the main topic of the course: modern Krylov subspace methods. The main ideas of these methods will be explained and how they lead to efficient solvers. Solution algorithms for linear systems that will be discussed include CG, GMRES, CGS, Bi-CGSTAB, Bi-CGSTAB(l) and IDR(s). Furthermore several preconditioning and deflation techniques will be explained. For large scale eigenvalue problems the Lanczos methods, Arnoldi's method and the Jacobi-Davidson method will be treated. |
| Organization | 14 lectures. Each lecture consists of instruction and (computer) assignments. |
| Examination | quizzes, a homework assignment and a final project assignment. |
| Literature | Lecture notes and hand-outs will be provided by the instructors. Recommended literature: "Matrix Computations" by Gene H. Golub and Charles F. van Loan. The John Hopkins University Press, Baltimore and London, 1996 "Iterative Krylov Methods for Large Linear Systems" by Henk A. van der Vorst, Cambridge University Press, Cambridge, 2003 |
| Prerequisites | Good knowledge of linear algebra and of programming in Matlab |