|
|
|
||
|
The first course of numerical analysis for students of computer science. Topics: approximaton of continuous functions, numerical qudrature, differentiation and methods for solving ordinary differential equations, methods of numerical linear algebra - decomposition of matrices, solving systems of linear equations, eigenvalue problem. Introduction to numerical methods for solving partial differential equations.
Last update: T_KNM (17.05.2008)
|
|
||
|
The course gives students a knowledge of fundamentals of numerical mathematics. Last update: T_KNM (17.05.2008)
|
|
||
|
It is necessary to obtain the course-credit before passing the exam.
To get the course-credit, one needs to obtain 12 points. The points will be awarded for:
Last update: Pozza Stefano, Dr., Ph.D. (01.02.2022)
|
|
||
|
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. Last update: Kučera Václav, doc. RNDr., Ph.D. (29.10.2019)
|
|
||
|
Lectures and tutorials in a lecture hall. Last update: T_KNM (17.05.2008)
|
|
||
|
The written exam has theoretical and practical parts. The examination requirements are given by the topics in the syllabus, to the extent to which they were taught in the course. Last update: Pozza Stefano, Dr., Ph.D. (15.02.2025)
|
|
||
|
Approximations 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, Gauss quadrature.
Methods for solving nonlinear equations, Newton method, proof of convergence of Newton method, method of successive approximations for nonlinear equations, roots of polynomials, 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 - the conjugate gradient method, the steepest descent method. Last update: Pozza Stefano, Dr., Ph.D. (31.01.2022)
|
|
||
|
There are no special entry requirements. Last update: T_KNM (17.05.2008)
|