Abstract
A new endpoint-corrected rule for the Clenshaw–Curtis (C–C) quadrature is proposed to improve the convergence rate. The error behavior is compared, analytically and numerically, to the C–C rule and related quadrature rules: the Fejér rules of the first and second kind and the Basu rule.
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Acknowledgments
We thank Professor David Levin of Tel Aviv University for his helpful comments for improving English of the manuscript. We are grateful to Professor Sotirios E. Notaris of University of Athens for his detailed and constructive comments and for the suggestion which inspired us to prove that the weights \(v_j\) in Theorem 3 are all positive for any \(n\), not only for \(n\rightarrow \infty \). We also thank the reviewers for their valuable advices, which led to significant improvement of the presentation.
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Hasegawa, T., Sugiura, H. Error estimate for a corrected Clenshaw–Curtis quadrature rule. Numer. Math. 130, 135–149 (2015). https://doi.org/10.1007/s00211-014-0660-y
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DOI: https://doi.org/10.1007/s00211-014-0660-y