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
Abbreviations used:
Semester:
- W ... winter semester (usually October - February)
- S ... spring semester (usually March - June)
- W,S ... both semesters
Mode of completion of the course:
- A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
- GA ... Graded Assessment (a grade is awarded for this course)
- EX ... Examination (a grade is awarded for this course)
- A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)
Weekly load (hours per week):
- P ... lecture
- C ... seminar
- L ... laboratory
- R ... proseminar
- S ... seminar