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Matematicheskie Trudy, 2004, Volume 7, Number 2, Pages 109–125 (Mi mt79)  
Asymptotics of the Errors of Complicated Cubature Formulas

V. I. Polovinkin

Krasnoyarsk State Technical University
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Abstract: Convergence is studied of complicated cubature formulas at an arbitrary function of the classes $W_p^m(\Omega)$. Some formulas are deduced for the principal terms of integration errors. As a rule, the lattices of nodes are not assumed to be rectangular. The results are generalized to weighted cubature formulas.
Key words: quadrature processes, Sobolev spaces, cubature formulas, interpolation operators.
Received: 21.01.2003
Bibliographic databases:
UDC: 517.3+519.6
Language: Russian
Citation: V. I. Polovinkin, “Asymptotics of the Errors of Complicated Cubature Formulas”, Mat. Tr., 7:2 (2004), 109–125; Siberian Adv. Math., 15:1 (2005), 74–90
Citation in format AMSBIB
\Bibitem{Pol04}
\by V.~I.~Polovinkin
\paper Asymptotics of the Errors of Complicated Cubature Formulas
\jour Mat. Tr.
\yr 2004
\vol 7
\issue 2
\pages 109--125
\mathnet{http://mi.mathnet.ru/mt79}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2124542}
\transl
\jour Siberian Adv. Math.
\yr 2005
\vol 15
\issue 1
\pages 74--90
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    		Математические труды Siberian Advances in Mathematics
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