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.KeywordsOrthogonal PolynomialChebyshev PolynomialProduct FormulaCubature FormulaOuter OperatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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