SubjectsSubjects(version: 916)
Course, academic year 2021/2022
Numerical Linear Algebra - P413002
Title: Numerická lineární algebra
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2021
Semester: both
Points: 0
E-Credits: 0
Examination process:
Hours per week, examination: 3/0, other [HT]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
For type: doctoral
Note: course is intended for doctoral students only
can be fulfilled in the future
you can enroll for the course in winter and in summer semester
Guarantor: Červená Lenka RNDr. Ph.D.
Interchangeability : D413018
Is interchangeable with: AP413002
Annotation -
Last update: Janovská Drahoslava prof. RNDr. CSc. (24.09.2018)
The lectures aim to extend 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.
Aim of the course -
Last update: Janovská Drahoslava prof. RNDr. CSc. (24.09.2018)

Students' skills

They will be familiar with problems of linear algebra, especially they will know the properties and calculation of own numbers and own vectors

They will be able to choose the appropriate method for solving linear system equations

They will know the principles of conditionality and stability of systems of linear algebraic equations.

Literature -
Last update: Janovská Drahoslava prof. RNDr. CSc. (06.06.2018)

R : G. Strang: Differential Equations and Linear Algebra. Wellesley-Cambridge, 2014.Z: Cauley R.A.: Corrosion of Ceramics. Marcel Dekker, Inc. New York 1995;

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

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

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

Learning resources -
Last update: Janovská Drahoslava prof. RNDr. CSc. (06.06.2018)

Teaching methods -
Last update: Janovská Drahoslava prof. RNDr. CSc. (06.06.2018)

Lectures and seminars

Requirements to the exam -
Last update: Janovská Drahoslava prof. RNDr. CSc. (06.06.2018)

Project to solve a more complex linear algebra problem.

Syllabus -
Last update: Janovská Drahoslava prof. RNDr. CSc. (06.06.2018)

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.

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (16.09.2019)


Course completion requirements -
Last update: Janovská Drahoslava prof. RNDr. CSc. (24.09.2018)

Preparation and defense of an individual project combined with an oral exam