Some New Results Concerning the Classical Bernstein Cubature Formula
Keyword(s):
In this article, we present a solution to the approximation problem of the volume obtained by the integration of a bivariate function on any finite interval [a,b]×[c,d], as well as on any symmetrical finite interval [−a,a]×[−a,a] when a double integral cannot be computed exactly. The approximation of various double integrals is done by cubature formulas. We propose a cubature formula constructed on the base of the classical bivariate Bernstein operator. As a valuable tool to approximate any volume resulted by integration of a bivariate function, we use the classical Bernstein cubature formula. Numerical examples are given to increase the validity of the theoretical aspects.
2007 ◽
Vol 05
(02)
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pp. 95-122
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1999 ◽
Vol 41
(1)
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pp. 41-57
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2012 ◽
Vol 64
(6)
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pp. 1359-1377
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1932 ◽
Vol 28
(4)
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pp. 442-454
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