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Numerical Quadrature and Cubature 2 - NNUM239

Title:	Numerická kvadratura a kubatura 2
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2013 to 2017
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Josef Kofroň, CSc.
Classification:	Mathematics > Numerical Analysis
Interchangeability :	NMNV566

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: RNDr. Jan Kofroň, Ph.D. (26.04.2006)

Modern methods of calculation of one and multidimensional integrals.

Aim of the course -

Last update: KOFRON/MFF.CUNI.CZ (23.04.2008)

Getting knowledge about advanced methods on numerical integration and their applications.

Literature - Czech

Last update: T_KNM (17.05.2008)

Davis P.J., Rabinowitz P.: Methods of Numerical Integration, Academic Press, l983

Engels H.: Numerical Quadrature and Cubature, Academic Press, l980

Teaching methods -

Last update: T_KNM (17.05.2008)

Lectures in the classroom.

Requirements to the exam -

Last update: T_KNM (17.05.2008)

Examination according to the syllabus.

Syllabus -

Last update: T_KNM (17.05.2008)

Orthogonal polynomials. Definitions and their properties. Special systems of orthogonal polynomials, implicitly defined orthogonal polynomials. Numerical calculation of the zeros of orthogonal polynomials. N-dimensional orthogonal polynomials.

Interpolatory quadrature and cubature-preassigned nodes or weights. The Newton-Cotes quadrature and cubature, the existence of positive cubature formulae with given nodes.

Tschebyschev's problem, equally-weighted cubature formulae. Refined interpolatory quadrature. General Gauss quadrature with free or preassigned nodes.

Qudratures with minimal error norm. Approximate computation of indefinite integrals. Noninterpolatory quadrature.

Richardson extrapolation,Romberg's quadrature,numerical integration of rapidly oscillating functions. Automatic integration, adaptive methods.