Course Unit Code | 310-2420/01 |
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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 * | Second Year |
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Semester when the Course Unit is delivered | Winter 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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| KUC14 | prof. RNDr. Radek Kučera, Ph.D. |
Summary |
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The course is devoted to basic numerical methods of the linear algebra and the mathematical analysis. |
Learning Outcomes of the Course Unit |
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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 |
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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 |
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Required Reading: |
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[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: |
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[1] SÜLI, E., MAYERS, D., F. An Introduction to Numerical Analysis. Cambridge: University Press, 2003. ISBN 978-0521007948.
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[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.
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Planned learning activities and teaching methods |
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Lectures, Individual consultations, 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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Examination | Examination | 100 | 51 |