470-2210/01 – Numerical Linear Algebra 1 (NLA1)
Gurantor department | Department of Applied Mathematics | Credits | 6 |
Subject guarantor | Ing. Michal Merta, Ph.D. | Subject version guarantor | Ing. Michal Merta, Ph.D. |
Study level | undergraduate or graduate | | |
| | Study language | Czech |
Year of introduction | 2019/2020 | Year of cancellation | |
Intended for the faculties | FEI | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
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.
Teaching methods
Lectures
Tutorials
Project work
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.
Compulsory literature:
- J.D. Tebbens, I. Hnětynková, M. Plešinger, Z. Strakoš, P. Tichý - Analysis of Methods for Matrix Computations. Basic Methods. Matfyzpress Prague, 2012.
Recommended literature:
- G.H. Golab, C.F. Van Loan - Matrix Computations, 4th edition. The John Hopkins University Press, 2013.
Way of continuous check of knowledge in the course of semester
Test 10 pts.)
Project (20 pts.)
E-learning
Other requirements
Successful defense of a semestral project.
Students are familiar with fundamentals of linear algebra.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
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.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction