Course Unit Code | 470-2210/01 |
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Number of ECTS Credits Allocated | 6 ECTS credits |
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Type of Course Unit * | Compulsory |
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Level of Course Unit * | First Cycle |
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Year of Study * | First Year |
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Semester when the Course Unit is delivered | Summer Semester |
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Mode of Delivery | Face-to-face |
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Language of Instruction | Czech |
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Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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Name of Lecturer(s) | Personal ID | Name |
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| KAB002 | Ing. Pavla Hrušková, Ph.D. |
| MER126 | Ing. Michal Merta, Ph.D. |
Summary |
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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 |
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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 |
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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.
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Recommended or Required Reading |
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Required Reading: |
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- 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: |
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- G.H. Golab, C.F. Van Loan - Matrix Computations, 4th edition. The John Hopkins University Press, 2013.
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- Z. Dostál, V. Vondrák - Lineární algebra. Skripta VŠB-TU Ostrava, http://mi21.vsb.cz, 2012 |
Planned learning activities and teaching methods |
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Lectures, Tutorials, Project work |
Assesment methods and criteria |
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Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing |
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Credit and Examination | Credit and Examination | 100 (100) | 51 |
Credit | Credit | 30 (30) | 15 |
Písemný test | Written test | 10 | 0 |
Semestrální projekt | Project | 20 | 0 |
Examination | Examination | 70 (70) | 21 |
Písemná část | Written examination | 55 | 0 |
Ústní část | Oral examination | 15 | 0 |