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Numerical Linear Algebra - D413018

Title:	Numerická lineární algebra
Guaranteed by:	Department of Mathematics (413)
Faculty:	Faculty of Chemical Engineering
Actual:	from 2011 to 2020
Semester:	winter
Points:	winter s.:0
E-Credits:	winter s.:0
Examination process:	winter s.:
Hours per week, examination:	winter s.:0/0, other [HT]
Capacity:	unknown / unknown (unknown)
Min. number of students:	unlimited
Qualifications:
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Level:
Note:	course is intended for doctoral students only can be fulfilled in the future

Guarantor:	Janovská Drahoslava prof. RNDr. CSc.

Examination dates Schedule

Annotation -

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.

Last update: JANOVSKD (19.10.2015)

Literature -

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.

Last update: JANOVSKD (07.10.2015)

Syllabus -

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.

Last update: JANOVSKD (30.09.2015)