Abstract
Error estimates for cubature formulas are usually given in terms of higher derivatives (Peano-Sard) or in terms of analyticity properties (Davis-Hämmerlin). The approximation method has found little attention. We present the latter method in a generalized and refined form, based on biorthogonal systems (BOGS). The degrees of approximation and coefficient estimates connected with a BOGS lead to rather good and versatile inequalities for the error. More specifically, we consider Chebyshev polynomials, Clenshaw-Curtis procedures and product formulas. Estimates for the employed degrees of approximation are available in the theory of approximation, and these estimates can be supported or refined by numerical computation.
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© 1982 Birkhäuser Verlag Basel
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Haußmann, W., Zeller, K., Luik, E. (1982). Cubature Remainder and Biorthogonal Systems. In: Schempp, W., Zeller, K. (eds) Multivariate Approximation Theory II. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 61. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7189-1_16
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DOI: https://doi.org/10.1007/978-3-0348-7189-1_16
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7191-4
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