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Numerical methods

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

Course Unit Code310-2420/01
Number of ECTS Credits Allocated6 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *Second Year
Semester when the Course Unit is deliveredWinter 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
KUC14prof. RNDr. Radek Kučera, Ph.D.
Summary
The course is devoted to basic numerical methods of the linear algebra and the mathematical analysis.
Learning Outcomes of the Course Unit
Students completing the course will be able to: recognize problems that can be solved numerically; chose a suitable numerical method; decide on the correctness of computed results and on its influence by rounding errors, discretization errors, or errors of another type; identify numerically stable and unstable calculations and characterize them by the condition number; analyze numerical algorithms from the point of view of computational complexities and storage requirements; use the Matlab language and the standard Matlab libraries; propose algorithmically correct implementations of basic numerical methods, write it in the Matlab language, debug and test
Course Contents
1. Disciplines of numerical mathematics: continuous and discrete problems, discretization order; sources of error, rounding error, computer epsilon; numerical stability.
2. Approximation and interpolation of functions: polynomial interpolation, interpolation error; least squares approximation; uniform approximation, Bernstein polynomials, spline functions; modeling curves and surfaces, Bezier curves.
3. Rootfinding for nonlinear functions: geometric approach to rootfinding; fixed-point iterations and fixed point theorem; fundamental theorem of algebra, separations and calculations of polynomial roots; Newton's method for nonlinear systems.
4. Numerical integration and derivation: numerical differentiation, Richardson extrapolation; numerical quadrature formulas, error estimation, step size control; Romberg method; Gauss formulas.
5. Numerical linear algebra: solving linear systems using LU decomposition variants, inverse matrix; eigenvalues and eigenvectors calculation, spectral decomposition; singular value decomposition, orthogonal factorization, pseudoinverse.
6. Iterative methods for solving linear systems: linear methods Jacobi, Gauss-Seidel, relaxation; nonlinear methods, steepest descent method, conjugate gradient method, preconditioning.
Recommended or Required Reading
Required Reading:
[1] QUARTERONI, S., SACCO, R., SALERI, F. Numerical Mathematics. 2. vyd. New York: Springer, 2007. ISBN 978-3-540-49809-4.
[1] KUČERA, R. Numerické metody. Ostrava: VŠB–Technická univerzita Ostrava, 2007. ISBN 80-248-1198-7.
[2] VONDRÁK, V., POSPÍŠIL, L. Numerické metody I. 1. vyd. Ostrava: VŠB–Technická univerzita Ostrava, 2011. ISBN 80-248-2449-9.
[3] QUARTERONI, S., SACCO, R., SALERI, F. Numerical Mathematics. 2. vyd. New York: Springer, 2007. ISBN 978-3-540-49809-4.
Recommended Reading:
[1] SÜLI, E., MAYERS, D., F. An Introduction to Numerical Analysis. Cambridge: University Press, 2003. ISBN 978-0521007948.
[1] MÍKA, S., BRANDNER, M. Numerické metody I. 1. vyd. Plzeň: Západočeská univerzita, 2000. ISBN 80-7082-619-3.
[2] SÜLI, E., MAYERS, D., F. An Introduction to Numerical Analysis. Cambridge: University Press, 2003. ISBN 978-0521007948.
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials, Project work
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
ExaminationExamination100 51