Abstract
For functions with possibly low continuity there are two main principles to derive quadrature error bounds. One method involves degrees of approximation (or upper bounds for them), the other one is based on series expansions (e. g. Chebyshev series). Using biorthogonal systems we recently presented an error estimate (called BOGS method) which contains the above mentioned methods as special cases. In the present work we first choose Chebyshev polynomials in the biorthogonal system and derive error bounds for Pólya type quadratures. In the second part there are employed Legendre polynomials in order to treat Gauss rules and bilinear quadrature. We further show how to replace some of the Fourier coefficient functionate by point functional with lower norm.
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