Optimal quadrature formulas of closed type in the space $L_2^{(m)}(0,1)$
arXiv:1005.01631.22 citationsh-index: 1
Originality Synthesis-oriented
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Provides a theoretical solution for optimal quadrature in a specific function space, but the result is incremental as it extends known methods to a particular case.
The paper derives explicit representations for optimal coefficients of closed-type quadrature formulas with equally spaced nodes in the Sobolev space L2^{(m)}(0,1) for any natural numbers m and N, solving the Sard problem in this setting.
It is discussed the problem on construction of optimal quadrature formulas in the sense of Sard in the space $L_2^{(m)}(0,1)$, when the nodes of quadrature formulas are equally spaced. Here the representations of optimal coefficients for any natural numbers $m$ and $N$ are found.