MS-E1651: Numerical Matrix Computations
| Course name | Numerical Matrix Computations |
|---|---|
| Course code | MS-E1651 |
| Abbreviation | “NMC” |
| Period | I |
| Lecturer | Antti Hannukainen |
Description
The core subjects of the course are factorization of matrices numerically and error bound analysis. The course serves as an introduction to dealing with matrices numerically.
Course material
Official material
Lecture notes as a PDF and the book “Trefethen, Bau: Numerical Linear Algebra”.
Extra material
Contents and workload
Workload feels similar to Bachelor courses.
Overall workload
Weekly contents
| Week | Topics |
|---|---|
| 1 | Introduction, Permutation matrices, Block matrix notation, Gaussian elimination, Back-substitution, LU-factorisation |
| 2 | Cholesky factorisation, fill-in, fill-in reducing permutation, minimum degree ordering |
| 3 | Numerical stability analysis, Backward error analysis, floating-point representation, floating-point arithmetic model, round-off error |
| 4 | Numerical stability analysis, Backward error analysis, Back-substitution, Cholesky factorisation, QR-factorisation, Givens Rotation |
| 5 | Iterative solution method, Fixed-point iteration, Convergence, Conjugate Gradient method, Line search method, Gradient Descend |
| 6 | Iterative solution method, Conjugate Gradient method, orthogonal projection, error estimate, Krylov subspace |
Practicalities
The course can be completed by only participating in the exam or by a combination of an exam, homework submissions and participation in the exercise sessions.
Related courses
Official prerequisites
Recommended prerequisites: MS-A00XX, MS-A01XX, MS-A02XX, MS-C134X. The courses MS-A03XX and MS-C1540 may also be useful.
Additional prerequisites
Sufficient Matlab knowledge.
More like this
MS-E1653: Finite Element Method, MS-E1654: Computational Inverse Problems.