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Last update: T_KNM (19.05.2008)
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Last update: FEIST/MFF.CUNI.CZ (28.04.2008)
To give a basic knowledge in numerical mathematics |
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Last update: T_KNM (19.05.2008)
Stoer J., Bullirsch R.: Introduction to Numerical Analysis, Springer, l978 |
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Last update: T_KNM (19.05.2008)
Lectures and tutorials in a lecture hall. |
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Last update: T_KNM (19.05.2008)
Examination according to the syllabus. |
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Last update: T_KNM (19.05.2008)
Numerical methods of linear algebra. LU decomposition, elimination method, matrix iterative methods, power method .
Interpolation of functions. Lagrange and Hermite polynomials. Spline functions. Least-square approximation.
Qudrature formulas. Gaussian and Newton-Cotes formulas.
Solution of Nonlinear Equations.
Systems of linear difference equations, homogeneous, nohomogeneous systems, fundamental system of solutions, systems with constant coefficients.
Numerical solution of ordinary differential equations. a) One-step methods: Examples, general one-step methods, local discretization error, accumulated discretization error, convergence, consistency, error estimates, round-off errors, aposteriori error estimate, derivation of some formulae, Runge-Kutta methods. b) Multi-step methods, general framework, convergence, stability, consistency, order of the method, error estimates, derivation of some multi-step schemes.
Some optimization methods. Elements of convex analysis, steepest descent methods with constant and optimal step, convergence. |
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Last update: FEIST/MFF.CUNI.CZ (28.04.2008)
basic knowledge of calculus and linear algebra |