SubjectsSubjects(version: 877)
Course, academic year 2020/2021
Numerical Linear Algebra - AP413002
Title: Numerical Linear Algebra
Guaranteed by: Department of Mathematics (413)
Actual: from 2019
Semester: both
Points: 0
E-Credits: 0
Examination process:
Hours per week, examination: 3/0 other [hours/week]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
Language: English
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: Janovská Drahoslava prof. RNDr. CSc.
Interchangeability : D413018, P413002
Annotation -
Last update: Pátková Vlasta (08.06.2018)
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: Pátková Vlasta (08.06.2018)

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: Pátková Vlasta (08.06.2018)

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: Pátková Vlasta (08.06.2018)

Teaching methods -
Last update: Pátková Vlasta (08.06.2018)

Lectures and seminars

Requirements to the exam -
Last update: Pátková Vlasta (08.06.2018)

Project to solve a more complex linear algebra problem.

Syllabus -
Last update: Pátková Vlasta (08.06.2018)

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: Pátková Vlasta (08.06.2018)

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