2009
DOI: 10.1134/s0965542509010011
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Error estimates in S P for cubature formulas exact for haar polynomials in the two-dimensional case

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Cited by 5 publications
(6 citation statements)
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“…Thus in the case of N ∼ 2 d when d → ∞ the cubature formulas (3.1) of Haar degree d, studied in [10], have the best order of convergence δ N S * p , equal to N − 1 p . In particular, minimal cubature formulas, constructed in [7] satisfy the condition N ∼ 2 d when d → ∞.…”
Section: The Construction Of Minimal Cubature Formulasmentioning
confidence: 95%
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“…Thus in the case of N ∼ 2 d when d → ∞ the cubature formulas (3.1) of Haar degree d, studied in [10], have the best order of convergence δ N S * p , equal to N − 1 p . In particular, minimal cubature formulas, constructed in [7] satisfy the condition N ∼ 2 d when d → ∞.…”
Section: The Construction Of Minimal Cubature Formulasmentioning
confidence: 95%
“…In [6] the following property of cubature formulas of Haar degree d is proved, which characterizes the location of nodes of these formulas. …”
Section: The Construction Of Minimal Cubature Formulasmentioning
confidence: 98%
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“…The problem of constructing cubature formulas possessing the Haar d-property, i.e., formulas exact for Haar polynomials of degree at most d, was solved in the two-dimensional case in [11][12][13][14][15] under the condition that the weight function g(x 1 , x 2 ) ≡ 1. The error estimates for these cubature formulas was derived in [16]. In particular, in [16] the upper estimate for the norm of the error functional ∥δ N ∥ S * p was obtained for the mentioned cubature formulas:…”
Section: Introductionmentioning
confidence: 99%