Piecewise Hermite interpolation via barycentric coordinates

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• 作者：Salvatore Cuomo ; Ardelio Galletti ; Giulio Giunta…
• 关键词：Discrete data interpolation ; Hermite interpolation ; Piecewise ; defined functions ; Barycentric coordinates ; 41A05 ; 65D05 ; 68U05
• 刊名：Ricerche di Matematica
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：64
• 期：2
• 页码：303-319
• 全文大小：721 KB
• 参考文献：1.Cuomo, S., D鈥?Amore, L., Murli, A., Rizzardi, M.: Computation of the inverse Laplace transform based on a collocation method which uses only real values. J. Comput. Appl. Math. 198(1), 98鈥?15 (2007)MATH MathSciNet CrossRef
  2.Cuomo, S., Galletti, A., Giunta, G., Marcellino, L.: A novel triangle-based method for scattered data interpolation. Appl. Math. Sci. 8(133鈥?36), 6717鈥?724 (2014)
  3.Cuomo, S., Galletti, A., Giunta, G., Marcellino, L.: A class of piecewise interpolating functions based on barycentric coordinates. Ricer. Mat. 63(1), 87鈥?02 (2014)MathSciNet CrossRef
  4.Cuomo, S., Galletti, A., Giunta, G., Starace, A.: Surface reconstruction from scattered point via RBF interpolation on GPU. Computer Science and Information Systems (FedCSIS), 433鈥?40 (2013)
  5.D鈥橝more, L., Campagna, R., Galletti, A., Marcellino, L., Murli, A.: A smoothing spline that approximates Laplace transform functions only known on measurements on the real axis. Inverse Problems 28, 025007 (2012). doi:10.鈥?088/鈥?266-5611/鈥?8/鈥?/鈥?25007 . (37pp)MathSciNet CrossRef
  6.D鈥橝more, L., Campagna, R., Galletti, A., Murli, A., Rizzardi, M.: On the numerical approximation of the laplace transform function from real samples and its inversion. Numerical mathematics and advanced applications 2009, Springer, pp. 209鈥?16 (2009)
  7.Fasshauer, G.: Meshfree Approximation methods with MATLAB. Interdisciplinary Mathematical Sciences, vol. 6. River Edge, NJ, World Sientific Publishers (2007)
  8.Franke, R., Nielson, G.: Smooth interpolations of large data sets of scattered data. Int. J. Numer. Methods Eng. 15, 1691鈥?704 (1980)MATH MathSciNet CrossRef
  9.Meijering, E.H.W.: A chronology of interpolation: from ancient astronomy to modern signal and image processing. Proc. IEEE 90(3), 319鈥?42 (2002)CrossRef
  10.Murli, A., Cuomo, S., D鈥橝more, L., Galletti, A.: Numerical regularization of a real inversion formula based on the Laplace transform鈥檚 eigenfunction expansion of the inverse function. Inverse problems 23, 713鈥?31 (2007)MATH MathSciNet CrossRef
  11.Singh, P., Joshi, S.D., Patney, R.K., Saha, K.: Some studies on nonpolynomial interpolation and error analysis. Appl. Math. Comput. 244, 809鈥?21 (2014)MathSciNet CrossRef
  
• 作者单位：Salvatore Cuomo (2)
  Ardelio Galletti (1)
  Giulio Giunta (1)
  Livia Marcellino (1)
  
  2. Department of Mathematics and Applications 鈥淩. Caccioppoli鈥? University of Naples 鈥淔ederico II鈥? Via Cintia, Complesso Monte S. Angelo, 80126, Naples, Italy
  1. Department of Science and Technology, Centro Direzionale, University of Naples 鈥淧arthenope鈥? Isola C4, 80143, Naples, Italy
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Analysis
  Geometry
  Numerical Analysis
  Probability Theory and Stochastic Processes
  
• 出版者：Springer Milan
• ISSN：1827-3491

文摘

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. Keywords Discrete data interpolation Hermite interpolation Piecewise-defined functions Barycentric coordinates