Czech

3

Institute of Mathematics and Descriptive Geometry (MAT)

Not applicable.

Calculus as taught in the basic courses.

Not applicable.

Not applicable.

Not applicable.

1. Solving 1 linear algebraic equation – starting methods, method of stepwise approximation, method of tangents, method of secants. Speed of convergnce.
2. Linear spaces and operators, norms of vectors and matrices. Contractive mapping, Banach fixed-point theorem.
3. Solving systems of non-linear algebraic equations – simple iteration, Newton method. Eigenvalues and eigenvectors of square matrices – direct computation, power method, subspace iteration method.
4. Overview of methods used to solve systems of linear algebraic equations. Direct methods – Gauss elimination, LU-decomposition, Cholesky decomposition.
5. Band and rare systems. Conditionality of systems. QR-decomposition. Constructing inverse and pseudoinverse matrices.
6. Iteration methods – Jacobi iteration, Gauss-Seidel iteration. Relaxation methods. Method of conjugate gradients.
7. Functional spaces. Interpolating a function – Lagrange polynomial, Hermit polynomial.
8. Linear and cubic splines. Approximation of a function by the least-square method.
9. Numeric differentiation, limit extrapolation.
10. Numeric integration – rectangular, trapezoidal and Simpson rule. Romberg method, Gauss quadrature.
11. Boundary and initial problems in differential equtions. Method of grids.
12. Variational formulation. Ritz-Galerkin method, finite-element method.
13. Application to problems in engineerig and physics.

Not applicable.

Since the academic year 2004/2005, this course has no longer been availabl.

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Not applicable.

Not applicable.

DALÍK, Josef: Numerické metody. CERM Brno, ISBN 80-214-0646-1 1997

Not applicable.

13 hours, compulsory