Numerical Linear Algebra 1

Type of study	Bachelor
Language of instruction	Czech
Code	470-2210/01
Abbreviation	NLA1
Course title	Numerical Linear Algebra 1
Credits	6
Coordinating department	Department of Applied Mathematics
Course coordinator	doc. Ing. Dalibor Lukáš, Ph.D.

Subject syllabus

- Systems of linear equations
- Gaussian elimination method.
- LU, LDMT, LDLT, and Cholesky factorizations.
- Sparse matrices.
- Linear iterative solution methods (Jacobi, Gauss-Seidel, Richardson), convergence rates.
- Gradient iterative solvers (steepest descent, conjugate gradient methods).
- Preconditioning.
- QR decomposition (Gramm-Schmidt process, Givens and Householder transformations).
- Applications of QR decomposition (least squares method, singular decomposition, pseudoinverse)
- Eigenvalues and spectral decomposition (QR algorithm), power iteration method.

E-learning

Materials are available at https://homel.vsb.cz/~luk76

Literature

- J.D. Tebbens, I. Hnětynková, M. Plešinger, Z. Strakoš, P. Tichý - Analysis of Methods for Matrix Computations. Basic Methods. Matfyzpress Prague, 2012.

Advised literature

- G.H. Golab, C.F. Van Loan - Matrix Computations, 4th edition. The John Hopkins University Press, 2013.

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