| Area of Mathematics: | Computational and Applied Mathematics (ECAM) |
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| Semester: | 5ο | ||
| Course ID: | 52401 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 3 | Practice: 0 | Laboratory: 1 |
| ECTS : | 5 | ||
| Eclass: | For the course’s material, click here. | ||
| Instructors: | Aretaki Aikaterini | ||
Description
- Vector and matrix norms. Equivalence of norms. Linear system sensitivity. Condition number.
- Gaussian elimination, partial and complete pivoting. LU factorization, Cholesky factorization.
- Iterative methods for solving linear systems: Jacobi, Gauss-Seidel and SOR iterations. Krylov subspace methods, conjugate gradient method.
- QR factorization by Householder matrices and by Givens rotations. Singular value decomposition (SVD). Least squares problem, normal equations.
- Applications of matrix factorizations.
- Eigenvalue problem, power method. Bounds for the spectrum.
- Gershgorin discs. Pseudospectrum.
Bibliography
- Trefethen L. N., Bau D., Numerical Linear Algebra, SIAM, 1997.
- Demmel J. W., Applied Numerical Linear Algebra., SIAM, 1997. ISBN 0-89871-389-7.
- Higham D. J., Higham N. J., MATLAB Guide, Third edition, 2017. SIAM, 2000. ISBN 0-89871-469-9.
