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Lecturer(s)
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Černá Dana, doc. RNDr. Ph.D.
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Course content
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1. Basic concepts - numerical methods, types of errors, conditioning of the problem, algorithm complexity. 2. Numerical linear algebra - vector and matrix norms, conditioning of matrices, Gaussian elimination - complexity, stability, pivotation, tridiagonal matrices. 3. LU decomposition - complexity, stability, pivotating. Cholesky decomposition. 4. Numerical solution of nonlinear equations - bisection method, Newton's method. 5. Numerical solution of nonlinear equations - secant method, the Babylonian method. 6. Lagrange interpolation - Lagrange and Newton form, error estimate. 7. Hermite interpolation - Newton form, error estimate. Spline interpolation. 8. Function approximation by the method of least squares, system of normal equations. 9. Numerical integration - the rectangular rule, the trapezoidal rule, Simpson's rule. 10. Numerical differentiation - differences, error estimates. 11. Numerical solution of initial value problems - basic concepts, transforming the n-th order differential equation into a system of n simultaneous equations of the first order. 12. Euler method for initial value problems. 13. Revision - solving problems by numerical methods. 14. Test.
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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The subject focuses on basic numerical methods, e.g., direct and iterative methods for solving systems of linear algebraic equations, numerical solution of nonlinear equations, integration, and Euler method for solving differential equations.
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Prerequisites
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unspecified
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Assessment methods and criteria
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unspecified
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Recommended literature
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Duintjer Tebbens E. J. ,Hnětynková I.,Plešinger M.,Strakoš Z.,Tichý P. Analýza metod pro maticové výpočty: Základní metody. Matfyzpress, 2012.
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Ueberhuber, Ch. W.:. Numerical Computation 1, 2.. Berlin: Springer-Verlag, 1997.
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Vitásek, E.:. Numerické metody.. Praha: SNTL, 1987.
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