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<p>This paper considers general cubature formulas that include both function values and values of its derivatives of various orders. The asymptotic optimality of general cubature formulas with regular boundary layer in the Sobolev space <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L^m_p\)</EquationSource> </InlineEquation> for odd <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(m\)</EquationSource> </InlineEquation> is substantiated.</p>

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On the asymptotic optimality of general cubature formulas in Sobolev space \(L^m_p(E_n)\) for odd \(m\)

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Nima B. Tsyrenzhapov,
  • Alexander V. Urbakhanov

摘要

This paper considers general cubature formulas that include both function values and values of its derivatives of various orders. The asymptotic optimality of general cubature formulas with regular boundary layer in the Sobolev space \(L^m_p\) for odd \(m\) is substantiated.