Piecewise Hermite interpolation via barycentric coordinates
Abstract Piecewise interpolation methods, as spline or Hermite cubic interpolation methods, define the interpolating function by means of polynomial pieces and ensure that some regularity conditions hold at the break-points. In this paper, starting from a previous work, where we proposed a class of...
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| Autor*in: |
Cuomo, Salvatore [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Anmerkung: |
© Università degli Studi di Napoli "Federico II" 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Ricerche di matematica - Springer Milan, 1952, 64(2015), 2 vom: 23. Juni, Seite 303-319 |
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| Übergeordnetes Werk: |
volume:64 ; year:2015 ; number:2 ; day:23 ; month:06 ; pages:303-319 |
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10.1007/s11587-015-0233-0 |
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OLC2055582763 |
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| 520 | |a Abstract Piecewise interpolation methods, as spline or Hermite cubic interpolation methods, define the interpolating function by means of polynomial pieces and ensure that some regularity conditions hold at the break-points. In this paper, starting from a previous work, where we proposed a class of piecewise interpolating functions whose expression depends on the barycentric coordinates, we extend that approach to obtain an interpolant for which Hermite constraints are assigned. The underlying idea is to define the interpolant on each subinterval, by weighting two Taylor polynomials, centered at the endpoints, of a function that generated the Hermite conditions. The weights depend on a suitable function of the barycentric coordinates of the evaluation point. We show that the interpolating function inherits the properties of regularity from such a weight function. Moreover, we study the interpolation error and provide bounds in terms of both the degree of the Taylor polynomials and properties of the weight function. Numerical experiments confirm the theoretical results and show the reliability of the bounds provided for the interpolation error. | ||
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| 700 | 1 | |a Giunta, Giulio |4 aut | |
| 700 | 1 | |a Marcellino, Livia |4 aut | |
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10.1007/s11587-015-0233-0 doi (DE-627)OLC2055582763 (DE-He213)s11587-015-0233-0-p DE-627 ger DE-627 rakwb eng 510 VZ Cuomo, Salvatore verfasserin aut Piecewise Hermite interpolation via barycentric coordinates 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Università degli Studi di Napoli "Federico II" 2015 Abstract Piecewise interpolation methods, as spline or Hermite cubic interpolation methods, define the interpolating function by means of polynomial pieces and ensure that some regularity conditions hold at the break-points. In this paper, starting from a previous work, where we proposed a class of piecewise interpolating functions whose expression depends on the barycentric coordinates, we extend that approach to obtain an interpolant for which Hermite constraints are assigned. The underlying idea is to define the interpolant on each subinterval, by weighting two Taylor polynomials, centered at the endpoints, of a function that generated the Hermite conditions. The weights depend on a suitable function of the barycentric coordinates of the evaluation point. We show that the interpolating function inherits the properties of regularity from such a weight function. Moreover, we study the interpolation error and provide bounds in terms of both the degree of the Taylor polynomials and properties of the weight function. Numerical experiments confirm the theoretical results and show the reliability of the bounds provided for the interpolation error. Discrete data interpolation Hermite interpolation Piecewise-defined functions Barycentric coordinates Galletti, Ardelio aut Giunta, Giulio aut Marcellino, Livia aut Enthalten in Ricerche di matematica Springer Milan, 1952 64(2015), 2 vom: 23. Juni, Seite 303-319 (DE-627)129853259 (DE-600)280837-7 (DE-576)015154122 0035-5038 nnns volume:64 year:2015 number:2 day:23 month:06 pages:303-319 https://doi.org/10.1007/s11587-015-0233-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_62 GBV_ILN_2010 GBV_ILN_4036 AR 64 2015 2 23 06 303-319 |
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10.1007/s11587-015-0233-0 doi (DE-627)OLC2055582763 (DE-He213)s11587-015-0233-0-p DE-627 ger DE-627 rakwb eng 510 VZ Cuomo, Salvatore verfasserin aut Piecewise Hermite interpolation via barycentric coordinates 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Università degli Studi di Napoli "Federico II" 2015 Abstract Piecewise interpolation methods, as spline or Hermite cubic interpolation methods, define the interpolating function by means of polynomial pieces and ensure that some regularity conditions hold at the break-points. In this paper, starting from a previous work, where we proposed a class of piecewise interpolating functions whose expression depends on the barycentric coordinates, we extend that approach to obtain an interpolant for which Hermite constraints are assigned. The underlying idea is to define the interpolant on each subinterval, by weighting two Taylor polynomials, centered at the endpoints, of a function that generated the Hermite conditions. The weights depend on a suitable function of the barycentric coordinates of the evaluation point. We show that the interpolating function inherits the properties of regularity from such a weight function. Moreover, we study the interpolation error and provide bounds in terms of both the degree of the Taylor polynomials and properties of the weight function. Numerical experiments confirm the theoretical results and show the reliability of the bounds provided for the interpolation error. Discrete data interpolation Hermite interpolation Piecewise-defined functions Barycentric coordinates Galletti, Ardelio aut Giunta, Giulio aut Marcellino, Livia aut Enthalten in Ricerche di matematica Springer Milan, 1952 64(2015), 2 vom: 23. Juni, Seite 303-319 (DE-627)129853259 (DE-600)280837-7 (DE-576)015154122 0035-5038 nnns volume:64 year:2015 number:2 day:23 month:06 pages:303-319 https://doi.org/10.1007/s11587-015-0233-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_62 GBV_ILN_2010 GBV_ILN_4036 AR 64 2015 2 23 06 303-319 |
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10.1007/s11587-015-0233-0 doi (DE-627)OLC2055582763 (DE-He213)s11587-015-0233-0-p DE-627 ger DE-627 rakwb eng 510 VZ Cuomo, Salvatore verfasserin aut Piecewise Hermite interpolation via barycentric coordinates 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Università degli Studi di Napoli "Federico II" 2015 Abstract Piecewise interpolation methods, as spline or Hermite cubic interpolation methods, define the interpolating function by means of polynomial pieces and ensure that some regularity conditions hold at the break-points. In this paper, starting from a previous work, where we proposed a class of piecewise interpolating functions whose expression depends on the barycentric coordinates, we extend that approach to obtain an interpolant for which Hermite constraints are assigned. The underlying idea is to define the interpolant on each subinterval, by weighting two Taylor polynomials, centered at the endpoints, of a function that generated the Hermite conditions. The weights depend on a suitable function of the barycentric coordinates of the evaluation point. We show that the interpolating function inherits the properties of regularity from such a weight function. Moreover, we study the interpolation error and provide bounds in terms of both the degree of the Taylor polynomials and properties of the weight function. Numerical experiments confirm the theoretical results and show the reliability of the bounds provided for the interpolation error. Discrete data interpolation Hermite interpolation Piecewise-defined functions Barycentric coordinates Galletti, Ardelio aut Giunta, Giulio aut Marcellino, Livia aut Enthalten in Ricerche di matematica Springer Milan, 1952 64(2015), 2 vom: 23. Juni, Seite 303-319 (DE-627)129853259 (DE-600)280837-7 (DE-576)015154122 0035-5038 nnns volume:64 year:2015 number:2 day:23 month:06 pages:303-319 https://doi.org/10.1007/s11587-015-0233-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_62 GBV_ILN_2010 GBV_ILN_4036 AR 64 2015 2 23 06 303-319 |
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10.1007/s11587-015-0233-0 doi (DE-627)OLC2055582763 (DE-He213)s11587-015-0233-0-p DE-627 ger DE-627 rakwb eng 510 VZ Cuomo, Salvatore verfasserin aut Piecewise Hermite interpolation via barycentric coordinates 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Università degli Studi di Napoli "Federico II" 2015 Abstract Piecewise interpolation methods, as spline or Hermite cubic interpolation methods, define the interpolating function by means of polynomial pieces and ensure that some regularity conditions hold at the break-points. In this paper, starting from a previous work, where we proposed a class of piecewise interpolating functions whose expression depends on the barycentric coordinates, we extend that approach to obtain an interpolant for which Hermite constraints are assigned. The underlying idea is to define the interpolant on each subinterval, by weighting two Taylor polynomials, centered at the endpoints, of a function that generated the Hermite conditions. The weights depend on a suitable function of the barycentric coordinates of the evaluation point. We show that the interpolating function inherits the properties of regularity from such a weight function. Moreover, we study the interpolation error and provide bounds in terms of both the degree of the Taylor polynomials and properties of the weight function. Numerical experiments confirm the theoretical results and show the reliability of the bounds provided for the interpolation error. Discrete data interpolation Hermite interpolation Piecewise-defined functions Barycentric coordinates Galletti, Ardelio aut Giunta, Giulio aut Marcellino, Livia aut Enthalten in Ricerche di matematica Springer Milan, 1952 64(2015), 2 vom: 23. Juni, Seite 303-319 (DE-627)129853259 (DE-600)280837-7 (DE-576)015154122 0035-5038 nnns volume:64 year:2015 number:2 day:23 month:06 pages:303-319 https://doi.org/10.1007/s11587-015-0233-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_62 GBV_ILN_2010 GBV_ILN_4036 AR 64 2015 2 23 06 303-319 |
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10.1007/s11587-015-0233-0 doi (DE-627)OLC2055582763 (DE-He213)s11587-015-0233-0-p DE-627 ger DE-627 rakwb eng 510 VZ Cuomo, Salvatore verfasserin aut Piecewise Hermite interpolation via barycentric coordinates 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Università degli Studi di Napoli "Federico II" 2015 Abstract Piecewise interpolation methods, as spline or Hermite cubic interpolation methods, define the interpolating function by means of polynomial pieces and ensure that some regularity conditions hold at the break-points. In this paper, starting from a previous work, where we proposed a class of piecewise interpolating functions whose expression depends on the barycentric coordinates, we extend that approach to obtain an interpolant for which Hermite constraints are assigned. The underlying idea is to define the interpolant on each subinterval, by weighting two Taylor polynomials, centered at the endpoints, of a function that generated the Hermite conditions. The weights depend on a suitable function of the barycentric coordinates of the evaluation point. We show that the interpolating function inherits the properties of regularity from such a weight function. Moreover, we study the interpolation error and provide bounds in terms of both the degree of the Taylor polynomials and properties of the weight function. Numerical experiments confirm the theoretical results and show the reliability of the bounds provided for the interpolation error. Discrete data interpolation Hermite interpolation Piecewise-defined functions Barycentric coordinates Galletti, Ardelio aut Giunta, Giulio aut Marcellino, Livia aut Enthalten in Ricerche di matematica Springer Milan, 1952 64(2015), 2 vom: 23. Juni, Seite 303-319 (DE-627)129853259 (DE-600)280837-7 (DE-576)015154122 0035-5038 nnns volume:64 year:2015 number:2 day:23 month:06 pages:303-319 https://doi.org/10.1007/s11587-015-0233-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_62 GBV_ILN_2010 GBV_ILN_4036 AR 64 2015 2 23 06 303-319 |
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Piecewise Hermite interpolation via barycentric coordinates |
| abstract |
Abstract Piecewise interpolation methods, as spline or Hermite cubic interpolation methods, define the interpolating function by means of polynomial pieces and ensure that some regularity conditions hold at the break-points. In this paper, starting from a previous work, where we proposed a class of piecewise interpolating functions whose expression depends on the barycentric coordinates, we extend that approach to obtain an interpolant for which Hermite constraints are assigned. The underlying idea is to define the interpolant on each subinterval, by weighting two Taylor polynomials, centered at the endpoints, of a function that generated the Hermite conditions. The weights depend on a suitable function of the barycentric coordinates of the evaluation point. We show that the interpolating function inherits the properties of regularity from such a weight function. Moreover, we study the interpolation error and provide bounds in terms of both the degree of the Taylor polynomials and properties of the weight function. Numerical experiments confirm the theoretical results and show the reliability of the bounds provided for the interpolation error. © Università degli Studi di Napoli "Federico II" 2015 |
| abstractGer |
Abstract Piecewise interpolation methods, as spline or Hermite cubic interpolation methods, define the interpolating function by means of polynomial pieces and ensure that some regularity conditions hold at the break-points. In this paper, starting from a previous work, where we proposed a class of piecewise interpolating functions whose expression depends on the barycentric coordinates, we extend that approach to obtain an interpolant for which Hermite constraints are assigned. The underlying idea is to define the interpolant on each subinterval, by weighting two Taylor polynomials, centered at the endpoints, of a function that generated the Hermite conditions. The weights depend on a suitable function of the barycentric coordinates of the evaluation point. We show that the interpolating function inherits the properties of regularity from such a weight function. Moreover, we study the interpolation error and provide bounds in terms of both the degree of the Taylor polynomials and properties of the weight function. Numerical experiments confirm the theoretical results and show the reliability of the bounds provided for the interpolation error. © Università degli Studi di Napoli "Federico II" 2015 |
| abstract_unstemmed |
Abstract Piecewise interpolation methods, as spline or Hermite cubic interpolation methods, define the interpolating function by means of polynomial pieces and ensure that some regularity conditions hold at the break-points. In this paper, starting from a previous work, where we proposed a class of piecewise interpolating functions whose expression depends on the barycentric coordinates, we extend that approach to obtain an interpolant for which Hermite constraints are assigned. The underlying idea is to define the interpolant on each subinterval, by weighting two Taylor polynomials, centered at the endpoints, of a function that generated the Hermite conditions. The weights depend on a suitable function of the barycentric coordinates of the evaluation point. We show that the interpolating function inherits the properties of regularity from such a weight function. Moreover, we study the interpolation error and provide bounds in terms of both the degree of the Taylor polynomials and properties of the weight function. Numerical experiments confirm the theoretical results and show the reliability of the bounds provided for the interpolation error. © Università degli Studi di Napoli "Federico II" 2015 |
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Piecewise Hermite interpolation via barycentric coordinates |
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Galletti, Ardelio Giunta, Giulio Marcellino, Livia |
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Galletti, Ardelio Giunta, Giulio Marcellino, Livia |
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2024-07-04T02:33:58.776Z |
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