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Numerical Linear Algebra 1

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code470-2210/01
Number of ECTS Credits Allocated6 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
KAB002Ing. Pavla Hrušková, Ph.D.
MER126Ing. Michal Merta, Ph.D.
Summary
Linear algebra is a fundamental tool when formulating engineering problems and their efficient solution. This course is devoted to the related numerical methods and their efficient implementation.
Learning Outcomes of the Course Unit
Linear algebra stands behind computer solutions to complex engineering problems. The course Numerical Linear Algebra 1 aims at helping students to classify problems of linear algebra and choose a proper algorithm for the solution regarding stability (sensitivity of the output data on the inputs) and computational complexity.
Course Contents
1. Systems of linear equations (nonsingular, underdetermined, and overdetermined).
2. Gaussian elimination method.
3. LU and Cholesky factorizations.
4. Sparse matrices.
5. QR factorization (Givens and Householder transform).
6. Eigenvalues and spectral decomposition (QR and LR algorithm, shift).
7. Cauchy contour integral method.
8. Singular value decomposition, matrix pseudoiverse.
9. Linear iterative solution methods (Jacobi, Gauss-Seidel, Richardson), convergence rates.
10. Chebyshev semi-iterative method, convergence rate.
11. Krylov space, method of conjugate gradients.
12. Rate of convergence of the conjugate gradient method, preconditioning.
13. Tři-diagonalization, Lanczos method.
14. Presentation of students projects.
Recommended or Required Reading
Required Reading:
- J.D. Tebbens, I. Hnětynková, M. Plešinger, Z. Strakoš, P. Tichý - Analysis of Methods for Matrix Computations. Basic Methods. Matfyzpress Prague, 2012.
- J.D. Tebbens, I. Hnětynková, M. Plešinger, Z. Strakoš, P. Tichý - Analysis of Methods for Matrix Computations. Basic Methods. Matfyzpress Prague, 2012.
Recommended Reading:
- G.H. Golab, C.F. Van Loan - Matrix Computations, 4th edition. The John Hopkins University Press, 2013.
- Z. Dostál, V. Vondrák - Lineární algebra. Skripta VŠB-TU Ostrava, http://mi21.vsb.cz, 2012
Planned learning activities and teaching methods
Lectures, Tutorials, Project work
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit30 (30)15
                Písemný testWritten test10 0
                Semestrální projektProject20 0
        ExaminationExamination70 (70)21
                Písemná částWritten examination55 0
                Ústní částOral examination15 0