A sharp discrete convolution sum estimate
The paper by C. Lubich in Numer. Math. 2(52):129–145, 1988 is widely cited for its analysis of convolution quadrature rules for integrals with weakly singular kernels. This analysis depends on a key technical lemma (an upper bound on a discrete convolution sum) whose proof uses some advanced tools....
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Veröffentlicht in: | Communications in nonlinear science & numerical simulation 2023-02, Vol.117, p.106923, Article 106923 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | The paper by C. Lubich in Numer. Math. 2(52):129–145, 1988 is widely cited for its analysis of convolution quadrature rules for integrals with weakly singular kernels. This analysis depends on a key technical lemma (an upper bound on a discrete convolution sum) whose proof uses some advanced tools. In the present paper it will be shown that this lemma can be quickly proved in an elementary way; moreover, the new proof includes those cases that were excluded from the 1988 paper, and the bounds obtained are shown to be sharp. |
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ISSN: | 1007-5704 1878-7274 |
DOI: | 10.1016/j.cnsns.2022.106923 |