Mathematics for Applications+Numerical Methods 2

Course guarantor:

Petr Mayer

Lecturer:

Petr Mayer

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Numerical methods of numerical linear algabra and analysis

Requirements:

Syllabus of lectures:

Numerical algebra:

1.Roots of systems of nonlinear equations

2.Iterative method, Aitken's acceleration

3.Newton's method and modified Newton's method

4.Systems of linear algebraic equations

5.Eliminations techniques of Gauss type, Choleski decompostion

6.Systems with banded matrices, systems with positive definite matrices, systems with tridiagonal matrices

7.Fast methods

8.Systems with sparse matrices

9.Iterative methods

10. Splitting up methods, regular splittings

11.Jacobi, Gauss-Seidel and SOR methods

12.PCG and GMRES methods

13.Preconditioning

14.Mulrilvel methods for eliptic problems

15.Domain Decomposition Methods - DDM

16.Overlapping and nonoverlapping methods.

17.Neumann-Neumann type methods

18. Balanced DD

19. Fully Black Box of overlapping Schwarz method

20.Eigenvalue problem

21.Power method, Kellogg's proccess

22.LR and QR methods

23.Generalized eigenvalue problem

24.Inverse iteration

Numerical analysis:

1.Computations, rounding errors, numerical stability

2.Numerical quadrature, computation of Fourier coeficients

3.Numerical methods for initial value problem for ODE's and systems of ODE's.

4.Boundary value problem for PDE's and systems

5.Finite element and Boundary element methods

6.Evolution problems for PDE's, rational aproximation of exponential function

7.Euler and Implicit Euler methods, Crank-Nicholson method, methods of Runge-Kutta type

Optimization methods

1.Simplex method

2.Uzawa algorithm

3.

Syllabus of tutorials:

Study Objective:

Study materials:

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: