# Splines in Numerical Integration

• Volume: 24, Issue: 3-4, page 351-358
• ISSN: 0205-3217

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## Abstract

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AMS Subj. Classiﬁcation: 65D07, 65D30.We gave a short review of several results which are related to the role of splines (cardinal, centered or interpolating) in numerical integration. Results deal with the problem of approximate computation of the integrals with spline as a weight function, but also with the problem of approximate computation of the integrals without weight function. Besides, we presented an algorithm for calculation of the coeﬃcients of the polynomials which correspond to the cardinal B-spline of arbitrary order and described ﬁve methods for calculation of the moments in the case when cardinal B-spline of order m,m ∈ N, is a weight function.

## How to cite

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Udovičić, Zlatko. "Splines in Numerical Integration." Mathematica Balkanica New Series 24.3-4 (2010): 351-358. <http://eudml.org/doc/11356>.

@article{Udovičić2010,
abstract = {AMS Subj. Classiﬁcation: 65D07, 65D30.We gave a short review of several results which are related to the role of splines (cardinal, centered or interpolating) in numerical integration. Results deal with the problem of approximate computation of the integrals with spline as a weight function, but also with the problem of approximate computation of the integrals without weight function. Besides, we presented an algorithm for calculation of the coeﬃcients of the polynomials which correspond to the cardinal B-spline of arbitrary order and described ﬁve methods for calculation of the moments in the case when cardinal B-spline of order m,m ∈ N, is a weight function.},
author = {Udovičić, Zlatko},
journal = {Mathematica Balkanica New Series},
keywords = {Cardinal B-Spline; Coeﬃcients; Moments; Rectangular Rule; Interpolating Quadratic Spline; Hat Function; Cubic B-Spline; cardinal -spline; coefficients; moments; rectangular rule; interpolating quadratic spline; hat function; cubic -spline},
language = {eng},
number = {3-4},
pages = {351-358},
publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},
title = {Splines in Numerical Integration},
url = {http://eudml.org/doc/11356},
volume = {24},
year = {2010},
}

TY - JOUR
AU - Udovičić, Zlatko
TI - Splines in Numerical Integration
JO - Mathematica Balkanica New Series
PY - 2010
PB - Bulgarian Academy of Sciences - National Committee for Mathematics
VL - 24
IS - 3-4
SP - 351
EP - 358
AB - AMS Subj. Classiﬁcation: 65D07, 65D30.We gave a short review of several results which are related to the role of splines (cardinal, centered or interpolating) in numerical integration. Results deal with the problem of approximate computation of the integrals with spline as a weight function, but also with the problem of approximate computation of the integrals without weight function. Besides, we presented an algorithm for calculation of the coeﬃcients of the polynomials which correspond to the cardinal B-spline of arbitrary order and described ﬁve methods for calculation of the moments in the case when cardinal B-spline of order m,m ∈ N, is a weight function.
LA - eng
KW - Cardinal B-Spline; Coeﬃcients; Moments; Rectangular Rule; Interpolating Quadratic Spline; Hat Function; Cubic B-Spline; cardinal -spline; coefficients; moments; rectangular rule; interpolating quadratic spline; hat function; cubic -spline
UR - http://eudml.org/doc/11356
ER -

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