# Applied Numerical Mathematics

Semestr: Summer

Range: 2+2s

Completion:

Credits: 4

Programme type: Undefined

Study form: Fulltime

Course language:

### Summary:

This course is oriented towards practical applications of selected numerical methods demonstrated by examples. It helps to familiarize with basic numerical methods for the evaluation of functions, interpolation, extrapolation, computing of derivation and definite integral, solution of systems of linear algebraic equations, computing non-linear equations and their systems, and numerical data modeling. The next topics of the lectures are: errors, accuracy and stability of numerical computing and related error-free algorithms. Some cryptographic algorithms are also introduced.

### Keywords:

Numerical tasks of linear algebra, Error-free computation, Residue Number System

### Course syllabus:

1. Numerical computing in practice
2. Errors, accuracy, and stability of numerical computing
3. Data acquisition and statistical description of data
4. Evaluation of functions
5. Interpolation and extrapolation
6. Computing of derivation and definite integral
7. Solution of systems of linear algebraic equations
8. Computing non-linear equations
9. Solution of non-linear systems of equations
10. Modeling of data
11. Error-free computation
12. Modular arithmetic and error-free algorithms
13. Cryptographic algorithms
14. Random numbers

### Seminar syllabus:

1. Computing errors and floating point arithmetic
2. Stability of numerical computation
3. Pathological effects in numerical mathematics
4. Evaluation of functions
5. Interpolation and extrapolation
6. Computing of derivation and definite integral
7. Elimination methods of solution of linear algebraic equations
8. Iterative methods of solution of linear algebraic equations
9. Solution of non-linear systems of equations
10. Modeling of data parameters estimation
11. Error-free computation of functions
12. Error-free computation of systems of linear algebraic equations
13. Cryptographic algorithms
14. Monte Carlo methods

### Literature:

1. Lecture notes (in preparation)
2. http://www.ulib.org/webRoot/Books/Numerical_Recipes/
3. Gregory, R. T. - Krishnamurthy, E. V.: Methods and Applications of Error-free Computation, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo 1994
4. James, V. B. - Kenneth, J. A.: Parameter Estimation in Engineering and Science, John Wiley & Sons, New York, London, Sydney, Toronto 1977