Error estimates in S
P
for cubature formulas exact for haar polynomials in the two-dimensional case |
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Authors: | K A Kirillov M V Noskov |
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Institution: | (1) Siberian Federal University, ul. Kirenskogo 26, Krasnoyarsk, 660074, Russia |
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Abstract: | On the spaces S p , an upper estimate is found for the norm of the error functional δ N (f) of cubature formulas possessing the Haar d-property in the two-dimensional case. An asymptotic relation is proved for $ \left\| {\delta _N (f)} \right\|_{S_p^* } On the spaces S
p
, an upper estimate is found for the norm of the error functional δ
N
(f) of cubature formulas possessing the Haar d-property in the two-dimensional case. An asymptotic relation is proved for with the number of nodes N ∼ 2
d
, where d → ∞. For N ∼ 2
d
with d → ∞, it is shown that the norm of δ
N
for the formulas under study has the best convergence rate, which is equal to N
−1/p
.
Original Russian Text ? K.A. Kirillov, M.V. Noskov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi
Fiziki, 2009, Vol. 49, No. 1, pp. 3–13. |
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Keywords: | cubature formulas in the space of Haar functions error estimates for cubature formulas estimate for the best convergence rate |
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