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Numerical methods

Type of study Bachelor
Language of instruction English
Code 310-2420/02
Abbreviation NM
Course title Numerical methods
Credits 6
Coordinating department Department of Mathematics and Descriptive Geometry
Course coordinator prof. RNDr. Radek Kučera, Ph.D.

Subject syllabus

1. Disciplines of numerical mathematics: continuous and discrete problems, discretization order; sources of error, rounding error, computer epsilon; numerical stability.
2. Approximation and interpolation of functions: polynomial interpolation, interpolation error; least squares approximation; uniform approximation, Bernstein polynomials, spline functions; modeling curves and surfaces, Bezier curves.
3. Rootfinding for nonlinear functions: geometric approach to rootfinding; fixed-point iterations and fixed point theorem; fundamental theorem of algebra, separations and calculations of polynomial roots; Newton's method for nonlinear systems.
4. Numerical integration and derivation: numerical differentiation, Richardson extrapolation; numerical quadrature formulas, error estimation, step size control; Romberg method; Gauss formulas.
5. Numerical linear algebra: solving linear systems using LU decomposition variants, inverse matrix; eigenvalues and eigenvectors calculation, spectral decomposition; singular value decomposition, orthogonal factorization, pseudoinverse.
6. Iterative methods for solving linear systems: linear methods Jacobi, Gauss-Seidel, relaxation; nonlinear methods, steepest descent method, conjugate gradient method, preconditioning.

Literature

[1] QUARTERONI, S., SACCO, R., SALERI, F. Numerical Mathematics. 2. vyd. New York: Springer, 2007. ISBN 978-3-540-49809-4 .

Advised literature

[1] SÜLI, E., MAYERS, D., F. An Introduction to Numerical Analysis. Cambridge: University Press, 2003. ISBN 978-0521007948.