714-0552 – Numerical Methods and Statistics (NMaS)
Gurantor department | Department of Mathematics and Descriptive Geometry |
Subject guarantor | prof. RNDr. Radek Kučera, Ph.D. |
Study level | undergraduate or graduate |
Subject aims expressed by acquired skills and competences
The aim of this course is to acquaint students with the numerical solution of mathematical problems that arise in the other courses of their study and in the technical practice. The main accent lays in explanations of fundamental principles of numerical methods with emphases their general properties. It should lead to the ability in concrete situations to decide whether a numerical procedure is a suitable tool for solving a particular problem. An important ingredient of the course consists in the algorithmic implementation and in the utilization of existing computer programs specialized for numerical computations.
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
Summary
Basic problems of the numerical mathematics, errors in computations. Solving of
equation f(x)=0: bisection method, regula-falsi, iterative method, Newton´s
iteration. Numerical solution of systems of linear algebraic equations: LU-factorization, iterative methods, condition number of matrix, ill-conditioned matrices. Interpolation and approximation of functions: polynomial interpolation, interpolation by spline functions, least squares approximation. Numerical integration: Trapezoid rule, Simpson’s rule, Richardson extrapolation. Statistical processing data
with one or more arguments, empirical characteristics of statistical data, testing of hypotheses.
Regression analysis.
Compulsory literature:
Recommended literature:
1. Forsythe, G., E., Malcolm, M.,A., Moler, B., C.: Computer Methods for
Mathematical Computations. Prentice –Hall, Inc., Englewood Clifs, N.J. 07632, 1977.
2. Buchanan, J., L., Turner, P., R.: Numerical Method and Analysis. McGraw-Hill, Inc., New York, 1992.
3. Stoer, J., Burlish, R.: Introduction to Numerical Analysis. Springer-Verlag,
New York, Berlin, Heidelberg, 1992.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.