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Numerical Quadrature and Cubature - NMNV566

Title:	Numerická kvadratura a kubatura
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2014 to 2017
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Class:	M Mgr. NVM M Mgr. NVM > Volitelné
Classification:	Mathematics > Numerical Analysis
Incompatibility :	NNUM139
Interchangeability :	NNUM139
Is interchangeable with:	NNUM239, NNUM139

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Annotation -

Last update: T_KNM (27.04.2015)

Methods for evaluation of one-dimensional and multi-dimensional integrals, construction of quadrature formulae, error estimates, convergence, stability.

Literature - Czech

Last update: T_KNM (20.09.2013)

Josef Kofroň "Kvadraturní formule", SPN.

Philips J. Davis, Philips Rabinowitz "Methods of Numerical Integration" Academic Press, 1983.

H. Engels, Numerical Quadrature and Cubature" Academic Press, 1980.

Prem K. Kythe, Michael R. Schaeferkotter, Handbook of Computational Method for Integration, Chapman and Hall/CRC Press.

Syllabus -

Last update: T_KNM (27.04.2015)

Basic ideas, applications of quadrature formulae, historical notes.

Construction principles of quadrature formulae. Geometrical approach, Taylor expansion method, undetermined coefficients method, generating function method, interpolation quadratures, Monte-Carlo method, methods based on number theory.

Error analysis. Representation of error, Peano kernel, Sard kernel, remainder minimization, derivative free expression for error. Convergence of quadrature formulae.