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Last update: T_KNM (17.05.2008)
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Last update: T_KNM (17.05.2008)
The course gives students a knowledge of fundamentals of numerical mathematics. |
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Last update: FELCMAN/MFF.CUNI.CZ (11.02.2009)
Felcman J.: (2009). Numerická matematika, učební text k přednášce. Feistauer, M., Felcman, J., and Straškraba, I. (2003). Mathematical and Com- putational Methods for Compressible Flow. Oxford University Press, Oxford. Higham, N. (1989). The accuracy of solutions to triangular systems. SIAM J. Appl. Math., 26(5), 1252?1265. Quarteroni, A., Sacco, R., and Saleri, F. (2004). Numerical Mathematics (2nd edn), Volume 37 of Texts in Applied Mathematics. Springer, Berlin. ISBN 0-387-98959-5. Segethová, J. (2000). Základy numerické matematiky. Karolinum, Praha. Ueberhuber, W. (2000). Numerical Computation 1, 2: Methods, Software, and Analysis. Springer, Berlin. |
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Last update: T_KNM (17.05.2008)
Lectures and tutorials in a lecture hall. |
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Last update: doc. RNDr. Jiří Felcman, CSc. (13.10.2017)
Examination according to the syllabus. |
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Last update: doc. RNDr. Jiří Felcman, CSc. (08.06.2021)
Aproximations of functions in R, Lagrange interpolation polynomial, error of Lagrange interpolation, cubic spline, construction of natural cubic spline.
Numerical integration of functions, Newton-Cotes formulae, composed Newton-Cotes formulae, Romberg quadrature, Gauss quadrature.
Methods for solution of nonlinear equations, Newton method, proof of convergence of Newton method, method of successive approximations for nonlinear equations, roots of polynomial, Horner scheme.
Systems of linear equations, condition number of matrices, Gauss' elimination, LU decomposition, influence of rounding errors, Cholesky decomposition, QR decomposition, iterative methods for the solution of systems of linear equations.
Computation of matrix eigenvalues.
Numerical integration of ordinary differential equations. One-step methods, Runge-Kutta methods.
Gradient methods. |
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Last update: T_KNM (17.05.2008)
There are no special entry requirements. |