714-0552 – Numerical Methods and Statistics (NMaS)

Gurantor departmentDepartment of Mathematics and Descriptive Geometry
Subject guarantorprof. RNDr. Radek Kučera, Ph.D.
Study levelundergraduate or graduate
Subject version
Version codeYear of introductionYear of cancellationCredits
714-0552/00 1996/1997 1996/1997
714-0552/01 1999/2000 2005/2006 4
714-0552/02 1999/2000 2005/2006 3
714-0552/03 1999/2000 2005/2006 3
714-0552/04 1999/2000 2005/2006 4
714-0552/05 1999/2000 2005/2006 2
714-0552/06 1999/2000 2005/2006 4
714-0552/07 2004/2005 2019/2020 5
714-0552/08 2015/2016 2019/2020 5

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:

1. Boháč, Zdeněk: Numerical Methods and Statistics, VŠB – TUO, Ostrava 2005, ISBN 80-248-0803-X

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.