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- W2010381639 abstract "We investigate the error term of the dth degree compound quadrature formulae for finite-part integrals of the form ∫01x-pf(x) dx where p∈ and p ≥1. We are mainly interested in error bounds of the form |R[f]|≤c‖f(s)‖∞ with best possible constants c. It is shown that, for p∉ and n uniformly distributed nodes, the error behaves as O(np–s–1 for f∈Cs[0,1], p–1 <s ≤d+1. In a previous paper we have shown that this is not true for p∈ As an improvement, we consider the case of non-uniformly distributed nodes. Here, we show that for all p ≥ I and f∈Cs[0,1], an O(n–s) error estimate can be obtained in theory by a suitable choice of the nodes. A set of nodes with this property is staled explicitly. In practice, this graded mesh causes stability problems which are computationally expensive to overcome." @default.
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- W2010381639 date "1997-07-01" @default.
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- W2010381639 title "Generalized compound quadrature formulae for finite-part integrals" @default.
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- W2010381639 doi "https://doi.org/10.1093/imanum/17.3.479" @default.
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