Sharp Bounds for Lebesgue Constants of Barycentric Rational Interpolation at Equidistant Points
A rough analysis of the growth of the Lebesgue constant in the case of barycentric rational interpolation at equidistant interpolation points was made in [Bos et al. 11] and [Bos et al. 12], leading to the conclusion that it only grows logarithmically. Here we give a fine analysis, obtaining the pre...
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| Autor*in: |
Ibrahimoglu, B. Ali [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Rechteinformationen: |
Nutzungsrecht: © Taylor & Francis 2016 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Experimental mathematics - Natick, Mass. : Peters, 1992, 25(2016), 3, Seite 347 |
|---|---|
| Übergeordnetes Werk: |
volume:25 ; year:2016 ; number:3 ; pages:347 |
| Links: |
|---|
| DOI / URN: |
10.1080/10586458.2015.1072862 |
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| 520 | |a A rough analysis of the growth of the Lebesgue constant in the case of barycentric rational interpolation at equidistant interpolation points was made in [Bos et al. 11] and [Bos et al. 12], leading to the conclusion that it only grows logarithmically. Here we give a fine analysis, obtaining the precise growth formula for the Lebesgue constant under consideration, with γ being the Euler constant. The similarity between barycentric rational interpolation at equidistant points and polynomial interpolation at Chebyshev nodes (or the like) is remarkable. After revisiting the polynomial interpolation case in Section 1 and introducing the barycentric rational interpolation case in Section 2, tight lower and upper bound estimates are given in Section 3. These fine results could only be formulated after performing very high-order numerical experiments in exact arithmetic. In Section 4, we indicate that the result can be extended to the rational interpolants introduced by Floater and Hormann in [Floater and Hormann 07]. Finally, the proof of the new tight bounds is detailed in Section 5. | ||
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10.1080/10586458.2015.1072862 doi PQ20161012 (DE-627)OLC1979424691 (DE-599)GBVOLC1979424691 (PRQ)i929-bcab955dac0b5ca994cb8f3515eb93fe65dbd9e95175a3bf59f125ed4d1703b10 (KEY)0214189220160000025000300347sharpboundsforlebesgueconstantsofbarycentricration DE-627 ger DE-627 rakwb eng 510 DNB Ibrahimoglu, B. Ali verfasserin aut Sharp Bounds for Lebesgue Constants of Barycentric Rational Interpolation at Equidistant Points 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier A rough analysis of the growth of the Lebesgue constant in the case of barycentric rational interpolation at equidistant interpolation points was made in [Bos et al. 11] and [Bos et al. 12], leading to the conclusion that it only grows logarithmically. Here we give a fine analysis, obtaining the precise growth formula for the Lebesgue constant under consideration, with γ being the Euler constant. The similarity between barycentric rational interpolation at equidistant points and polynomial interpolation at Chebyshev nodes (or the like) is remarkable. After revisiting the polynomial interpolation case in Section 1 and introducing the barycentric rational interpolation case in Section 2, tight lower and upper bound estimates are given in Section 3. These fine results could only be formulated after performing very high-order numerical experiments in exact arithmetic. In Section 4, we indicate that the result can be extended to the rational interpolants introduced by Floater and Hormann in [Floater and Hormann 07]. Finally, the proof of the new tight bounds is detailed in Section 5. Nutzungsrecht: © Taylor & Francis 2016 equidistant nodes barycentric rational interpolation linear interpolation preassigned poles Cuyt, Annie oth Enthalten in Experimental mathematics Natick, Mass. : Peters, 1992 25(2016), 3, Seite 347 (DE-627)165670231 (DE-600)1150871-1 (DE-576)034201777 1058-6458 nnns volume:25 year:2016 number:3 pages:347 http://dx.doi.org/10.1080/10586458.2015.1072862 Volltext http://www.tandfonline.com/doi/abs/10.1080/10586458.2015.1072862 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2088 GBV_ILN_2244 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4323 AR 25 2016 3 347 |
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10.1080/10586458.2015.1072862 doi PQ20161012 (DE-627)OLC1979424691 (DE-599)GBVOLC1979424691 (PRQ)i929-bcab955dac0b5ca994cb8f3515eb93fe65dbd9e95175a3bf59f125ed4d1703b10 (KEY)0214189220160000025000300347sharpboundsforlebesgueconstantsofbarycentricration DE-627 ger DE-627 rakwb eng 510 DNB Ibrahimoglu, B. Ali verfasserin aut Sharp Bounds for Lebesgue Constants of Barycentric Rational Interpolation at Equidistant Points 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier A rough analysis of the growth of the Lebesgue constant in the case of barycentric rational interpolation at equidistant interpolation points was made in [Bos et al. 11] and [Bos et al. 12], leading to the conclusion that it only grows logarithmically. Here we give a fine analysis, obtaining the precise growth formula for the Lebesgue constant under consideration, with γ being the Euler constant. The similarity between barycentric rational interpolation at equidistant points and polynomial interpolation at Chebyshev nodes (or the like) is remarkable. After revisiting the polynomial interpolation case in Section 1 and introducing the barycentric rational interpolation case in Section 2, tight lower and upper bound estimates are given in Section 3. These fine results could only be formulated after performing very high-order numerical experiments in exact arithmetic. In Section 4, we indicate that the result can be extended to the rational interpolants introduced by Floater and Hormann in [Floater and Hormann 07]. Finally, the proof of the new tight bounds is detailed in Section 5. Nutzungsrecht: © Taylor & Francis 2016 equidistant nodes barycentric rational interpolation linear interpolation preassigned poles Cuyt, Annie oth Enthalten in Experimental mathematics Natick, Mass. : Peters, 1992 25(2016), 3, Seite 347 (DE-627)165670231 (DE-600)1150871-1 (DE-576)034201777 1058-6458 nnns volume:25 year:2016 number:3 pages:347 http://dx.doi.org/10.1080/10586458.2015.1072862 Volltext http://www.tandfonline.com/doi/abs/10.1080/10586458.2015.1072862 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2088 GBV_ILN_2244 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4323 AR 25 2016 3 347 |
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10.1080/10586458.2015.1072862 doi PQ20161012 (DE-627)OLC1979424691 (DE-599)GBVOLC1979424691 (PRQ)i929-bcab955dac0b5ca994cb8f3515eb93fe65dbd9e95175a3bf59f125ed4d1703b10 (KEY)0214189220160000025000300347sharpboundsforlebesgueconstantsofbarycentricration DE-627 ger DE-627 rakwb eng 510 DNB Ibrahimoglu, B. Ali verfasserin aut Sharp Bounds for Lebesgue Constants of Barycentric Rational Interpolation at Equidistant Points 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier A rough analysis of the growth of the Lebesgue constant in the case of barycentric rational interpolation at equidistant interpolation points was made in [Bos et al. 11] and [Bos et al. 12], leading to the conclusion that it only grows logarithmically. Here we give a fine analysis, obtaining the precise growth formula for the Lebesgue constant under consideration, with γ being the Euler constant. The similarity between barycentric rational interpolation at equidistant points and polynomial interpolation at Chebyshev nodes (or the like) is remarkable. After revisiting the polynomial interpolation case in Section 1 and introducing the barycentric rational interpolation case in Section 2, tight lower and upper bound estimates are given in Section 3. These fine results could only be formulated after performing very high-order numerical experiments in exact arithmetic. In Section 4, we indicate that the result can be extended to the rational interpolants introduced by Floater and Hormann in [Floater and Hormann 07]. Finally, the proof of the new tight bounds is detailed in Section 5. Nutzungsrecht: © Taylor & Francis 2016 equidistant nodes barycentric rational interpolation linear interpolation preassigned poles Cuyt, Annie oth Enthalten in Experimental mathematics Natick, Mass. : Peters, 1992 25(2016), 3, Seite 347 (DE-627)165670231 (DE-600)1150871-1 (DE-576)034201777 1058-6458 nnns volume:25 year:2016 number:3 pages:347 http://dx.doi.org/10.1080/10586458.2015.1072862 Volltext http://www.tandfonline.com/doi/abs/10.1080/10586458.2015.1072862 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2088 GBV_ILN_2244 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4323 AR 25 2016 3 347 |
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Sharp Bounds for Lebesgue Constants of Barycentric Rational Interpolation at Equidistant Points |
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Sharp Bounds for Lebesgue Constants of Barycentric Rational Interpolation at Equidistant Points |
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Ibrahimoglu, B. Ali |
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Experimental mathematics |
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Ibrahimoglu, B. Ali |
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Ibrahimoglu, B. Ali |
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10.1080/10586458.2015.1072862 |
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510 |
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sharp bounds for lebesgue constants of barycentric rational interpolation at equidistant points |
| title_auth |
Sharp Bounds for Lebesgue Constants of Barycentric Rational Interpolation at Equidistant Points |
| abstract |
A rough analysis of the growth of the Lebesgue constant in the case of barycentric rational interpolation at equidistant interpolation points was made in [Bos et al. 11] and [Bos et al. 12], leading to the conclusion that it only grows logarithmically. Here we give a fine analysis, obtaining the precise growth formula for the Lebesgue constant under consideration, with γ being the Euler constant. The similarity between barycentric rational interpolation at equidistant points and polynomial interpolation at Chebyshev nodes (or the like) is remarkable. After revisiting the polynomial interpolation case in Section 1 and introducing the barycentric rational interpolation case in Section 2, tight lower and upper bound estimates are given in Section 3. These fine results could only be formulated after performing very high-order numerical experiments in exact arithmetic. In Section 4, we indicate that the result can be extended to the rational interpolants introduced by Floater and Hormann in [Floater and Hormann 07]. Finally, the proof of the new tight bounds is detailed in Section 5. |
| abstractGer |
A rough analysis of the growth of the Lebesgue constant in the case of barycentric rational interpolation at equidistant interpolation points was made in [Bos et al. 11] and [Bos et al. 12], leading to the conclusion that it only grows logarithmically. Here we give a fine analysis, obtaining the precise growth formula for the Lebesgue constant under consideration, with γ being the Euler constant. The similarity between barycentric rational interpolation at equidistant points and polynomial interpolation at Chebyshev nodes (or the like) is remarkable. After revisiting the polynomial interpolation case in Section 1 and introducing the barycentric rational interpolation case in Section 2, tight lower and upper bound estimates are given in Section 3. These fine results could only be formulated after performing very high-order numerical experiments in exact arithmetic. In Section 4, we indicate that the result can be extended to the rational interpolants introduced by Floater and Hormann in [Floater and Hormann 07]. Finally, the proof of the new tight bounds is detailed in Section 5. |
| abstract_unstemmed |
A rough analysis of the growth of the Lebesgue constant in the case of barycentric rational interpolation at equidistant interpolation points was made in [Bos et al. 11] and [Bos et al. 12], leading to the conclusion that it only grows logarithmically. Here we give a fine analysis, obtaining the precise growth formula for the Lebesgue constant under consideration, with γ being the Euler constant. The similarity between barycentric rational interpolation at equidistant points and polynomial interpolation at Chebyshev nodes (or the like) is remarkable. After revisiting the polynomial interpolation case in Section 1 and introducing the barycentric rational interpolation case in Section 2, tight lower and upper bound estimates are given in Section 3. These fine results could only be formulated after performing very high-order numerical experiments in exact arithmetic. In Section 4, we indicate that the result can be extended to the rational interpolants introduced by Floater and Hormann in [Floater and Hormann 07]. Finally, the proof of the new tight bounds is detailed in Section 5. |
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| title_short |
Sharp Bounds for Lebesgue Constants of Barycentric Rational Interpolation at Equidistant Points |
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http://dx.doi.org/10.1080/10586458.2015.1072862 http://www.tandfonline.com/doi/abs/10.1080/10586458.2015.1072862 |
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