Code: D01MTN2 Mathematics for Applications+Numerical Methods 2
Lecturer: doc. RNDr. Petr Mayer Ph.D. Weekly load: 4P Completion: EX
Department: 11101 Credits: 4 Semester: S
Description:
Numerical methods of numerical linear algabra and analysis
Contents:
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.
Keywords:
direct methods, iterative methods, Gauss elimination, FEM, eigenvalue problem, boundary value problem

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