Summary
A general cubature formula with an arbitrary preassigned weight function is derived using monosplines and integration by parts. The problem of determining the best cubature is formulated in terms of monosplines of least deviation and a solution to the problem is given by Theorem 3 below. This theorem may also be viewed as an optimal property of a new kind of two-dimensional spline interpolation.
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This work was done while the author was working at CERN, Geneva, Switzerland
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El Tom, M.E.A. On best cubature formulas and spline interpolation. Numer. Math. 32, 291–305 (1979). https://doi.org/10.1007/BF01397003
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DOI: https://doi.org/10.1007/BF01397003