Abstract
We study some cubature formulae for integrals on I 2 = [-1, 1]2 that use two types of information for the integrand: line integrals over either the boundary of I 2 or the coordinate axes, and evaluations at the points of a uniform grid. The error of these cubature formulae is analyzed, in particular the exact Peano constants are found for some classes of functions of low smoothness.
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Gushev, V., Nikolov, G. (2001). Some Cubature Formulae Using Mixed Type Data. In: Haussmann, W., Jetter, K., Reimer, M. (eds) Recent Progress in Multivariate Approximation. ISNM International Series of Numerical Mathematics, vol 137. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8272-9_13
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DOI: https://doi.org/10.1007/978-3-0348-8272-9_13
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9498-2
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