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Last update: G_M (16.05.2012)
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Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (08.06.2015)
To give a basic knowledge in numerical mathematics. |
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Last update: doc. RNDr. Václav Kučera, Ph.D. (29.10.2019)
Credit requirements:
at seminars, students will be given 6 tasks, which they solve at home. They will submit the solved task (electronically or on paper) no later than one week before the beginning of their exercise to the tutor.
They can get 0 to 6 points for each task. To obtain the credit it is necessary to obtain at least 2/3 points, ie 24.
The 'nature of the examination of the course' excludes the repetition of that examination, POS, Article 8 (2) |
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Last update: doc. RNDr. Václav Kučera, Ph.D. (30.09.2019)
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Last update: G_M (27.04.2012)
Lectures and tutorials in a lecture hall. |
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Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (06.10.2017)
Examination according to the syllabus. |
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Last update: doc. RNDr. Václav Kučera, Ph.D. (28.08.2023)
1. What is numerical mathematics. Examples of applications.
2. Problem types and errors (forward, backward, residual). Stability of algorithms.
3. Schur theorem and its consequences.
4. Orthogonal transformations and QR factorization.
5. Least-squares problems and their solution by SVD and QR factorization.
6. Partial eigenvalue problem. Power method, Arnoldi and Lanczos method.
7. Systems of linear algebraic equations. LU factorization and its stability. Stationary iterative methods.
8. Nonlinear algebraic equations, Newton's method, fixed point iteration.
9. Numerical optimization, descent methods, Newton's method.
10. Orthogonal polynomials.
11. Interpolation of functions, Lagrange interpolation, spline functions.
12. Numerical quadrature, Newton-Cotes and Gauss formulas.
13. Numerical methods for ordinary differential equations, single step and Runge-Kutta methods, multistep methods, stability, orders. |
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Last update: G_M (27.04.2012)
basic knowledge of calculus and linear algebra |