SubjectsSubjects(version: 877)
Course, academic year 2020/2021
Numerical Linear Algebra - D413018
Title: Numerická lineární algebra
Guaranteed by: Department of Mathematics (413)
Actual: from 2011
Semester: winter
Points: winter s.:0
E-Credits: winter s.:0
Examination process: winter s.:
Hours per week, examination: winter s.:0/0 other [hours/week]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
For type:  
Note: course is intended for doctoral students only
can be fulfilled in the future
Guarantor: Janovská Drahoslava prof. RNDr. CSc.
Z//Is interchangeable with: AP413002, P413002
Annotation -
Last update: Janovská Drahoslava prof. RNDr. CSc. (19.10.2015)
The lectures aim to expand the student's view to the field of numerical linear algebra. All of the most important topics in the field are covered, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability.
Literature -
Last update: Janovská Drahoslava prof. RNDr. CSc. (07.10.2015)

R. A. Horn and C. R. Johnson, Matrix analysis, Cambridge University Press, Cambridge, 1992.

G. H. Golub, C. F. Van Loan: Matrix Computations, 3-rd ed., The John Hopkins University Press, 2012.

L.N. Trefethen, D. Bau III: Numerical Linear Algebra. SIAM Philadelphia, 1997

G. Strang: Differential Equations and Linear Algebra. Wellesley-Cambridge, 2014.

Syllabus -
Last update: Janovská Drahoslava prof. RNDr. CSc. (30.09.2015)

1. Eigenvalues, Singular Values, The Singular Value Decomposition.

2. QR Factorization.

3. Gram-Schmidt Orthogonalization.

4. Householder Triangularization.

5. Least Squares Problems.

6. Conditioning and Condition Numbers, Stability.

7. Stability of Gaussian Elimination. Pivoting.

8. Cholesky Factorization.

9. Eigenvalue Problems.

10. Rayleigh Quotient, Inverse Iteration.

11. QR Algorithm.

12. The Arnoldi Iteration.

13. Conjugate Gradients.

14. Preconditioning.