# 714-0052/01 – Numerical Methods and Statistics (NMaS)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 4 Subject guarantor doc. RNDr. Zdeněk Boháč, CSc. Subject version guarantor doc. RNDr. Zdeněk Boháč, CSc. Study level undergraduate or graduate Requirement Compulsory Year 2 Semester winter Study language Czech Year of introduction 1999/2000 Year of cancellation 2005/2006 Intended for the faculties FBI Intended for study types Master
Instruction secured by
BOH10 doc. RNDr. Zdeněk Boháč, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

### Subject aims expressed by acquired skills and competences

This course is closed.

### 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, roots of polynomials. Numerical solution of systems of linear algebraic equations: LU-factorization, iterative methods, condition number of matrix, ill-conditioned matrices. Numerical solution of systems of nonlinear equations: Fixed-point iteration, Newton’s method. Interpolation and approximation of functions: Polynomial interpolation, interpolation by cubic spline functions, least squares approximation. Numerical integration: Trapezoid rule, Simpson’s rule, Richardson extrapolation, Monte Carlo method. Characteristics of population and sample, measures of central tendency, measures of dispersion and skewness, sampling distributions, point estimate, confidence interval, moment method, maximum likelihood method, testing hypotheses.

### Compulsory 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. ISBN 0-07-112922-7 [3] Stoer, J., Burlish, R.: Introduction to Numerical Analysis. Springer-Verlag, New York, Berlin, Heidelberg 1992. ISBN 0-387-97878-X [4] Triola, Mario, F.: Elementary Statistics. Benjamin/Cummings Publ. Comp., Inc., Redwood City, California 1989.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Problematika numerických výpočtů Zdroje a typy chyb, podmíněnost úlohy, numerická stabilita algoritmu. Metody řešení algebraických a transcendentních rovnic Separace kořenů, metoda půlení intervalu, metoda regula - falsi, Newtonova metoda, iterační metoda. Podmínky konvergence. Řešení soustav lineárních rovnic Normy matic, podmíněnost matic. LU rozklad. Metoda prosté iterace, Seidelova iterační metoda, podmínky konvergence. Interpolace a aproximace funkcí Polynomiální interpolace, interpolace pomocí spline funkcí. Aproximace metodou nejmenších čtverců, Čebyševova aproximace. Numerická kvadratura Lichoběžníková a Simpsonova metoda, Rombergova integrace, Richardsonova extrapolace. Adaptivní kvadraturní formule. Pseudonáhodná čísla a jejich generátory, výpočet integrálu metodou Monte Carlo. Řešení soustav nelineárních rovnic Prostá iterační metoda, Newtonova metoda. Podmínky konvergence. Zpracování statistického souboru s jedním a více argumenty Určení empirických charakteristik statistického souboru s jedním a více argumenty, korelační a regresní analýza. Odhady parametrů a testování hypotéz Momentová metoda, metoda maximální věrohodnosti, intervaly spolehlivosti. Testování hypotéz.

### Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 20 (20) 0
Written exam Written test 15  0
Examination Examination 80 (80) 0
Written examination Written examination 60  0
Oral Oral examination 20  0
Mandatory attendence parzicipation:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2004/2005 (M3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 2 Compulsory study plan
2004/2005 (M3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 2 Compulsory study plan
2003/2004 (M3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 2 Compulsory study plan
2003/2004 (M3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 2 Compulsory study plan

### Occurrence in special blocks

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