CAA: the Padua Points

• Brief description of the Padua points, with figure.
• Poster on interpolation and cubature at the Padua points.
• Software for interpolation and cubature at the Padua points.

Publications, preprints and abstracts concerning or related to the Padua points

• Bivariate polynomial interpolation on the square at new nodal sets
  preprint - M. Caliari, S. De Marchi and M. Vianello
  Appl. Math. Comput. 165/2 (2005), 261--274
  
  
• Bivariate Lagrange interpolation at the Padua points: the generating curve approach
  preprint - L. Bos, M. Caliari, S. De Marchi, M. Vianello and Y. Xu
  J. Approx. Theory 143 (2006), 15--25
  
  
• Bivariate Lagrange interpolation at the Padua points: computational aspects
  M. Caliari (with S. De Marchi, R. Montagna and M. Vianello)
  poster presented at the "1st Dolomites Workshop on Constructive Approximation and Applications" (Alba di Canazei, Trento (Italy), September 2006)
  
  
• Bivariate Lagrange interpolation at the Padua points: the ideal theory approach
  preprint - L. Bos, S. De Marchi, M. Vianello and Y. Xu
  Numer. Math. 108 (2007), 43--57
  
  
• Hyperinterpolation at Xu points and interpolation at Padua points in the square: computational aspects
  graduate thesis - R. Montagna (supervisors S. De Marchi and M. Caliari)
  University of Verona, 2007
  
  
• Some Recent Advances in Multivariate Polynomial Interpolation
  J.M. Carnicer and M. Gasca
  International Conference of Numerical Analysis and Applied Mathematics. AIP Conference Proceedings, Volume 936, pp. 7-9 (2007)
  
  
• Exact order of the Lebesgue constants for bivariate Lagrange interpolation at certain node systems
  B. Della Vecchia, G. Mastroianni and P. Vertesi
  Studia Sci. Math. Hungar., published online 2 September 2008
  
  
• Bivariate Lagrange interpolation at the Padua points: computational aspects
  preprint - M. Caliari, S. De Marchi and M. Vianello
  J. Comput. Appl. Math. 221 (2008), 284--292
  
  
• Nontensorial Clenshaw-Curtis cubature
  preprint - A. Sommariva, M. Vianello and R. Zanovello
  Numer. Algorithms 49 (2008), 409--427
  
  
• Algorithm 886: Padua2D: Lagrange Interpolation at Padua Points on Bivariate Domains
  preprint - M. Caliari, S. De Marchi and M. Vianello
  ACM Trans. Math. Software 35-3 (2008)
  
  
• Histogram Compression and Image Retrieval Through Padua Points Interpolation
  R. Montagna and G. Finlayson (University of East Anglia, UK)
  abstract of a talk presented at the "CGIV 2008/MCS/08 4th European Conference on Colour in Graphics, Imaging, and Vision" (Barcelona, June 2008)
  
  
• Near-optimal interpolation and quadrature in two variables: the Padua points
  M. Vianello (with M. Caliari, S. De Marchi, A. Sommariva)
  poster presented at the "5th European Congress of Mathematics" (Amsterdam, July 2008)
  
  
• Error formulas for multivariate rational interpolation
  X. Yang (Antwerp) (with A. Cuyt)
  abstract of a talk presented at the "ICCAM 2008" (Gent, July 2008)
  
  
• Efficient implementation of bivariate interpolation and cubature at Padua points
  M. Caliari (with S. De Marchi, A. Sommariva, M. Vianello)
  abstract of a talk presented at the "SIMAI 2008 (in cooperation with SIAM)" (Rome, September 2008)
  
  
• Optimal interpolation and Lp norm minimisation in colour indexing
  G. Finlayson and R. Montagna (University of East Anglia, UK)
  abstract of a poster presented at the "Sixteenth Color Imaging Conference" (Portland, November 2008)
  
  
• Issues in multivariate polynomial interpolation
  C. de Boor (Madison)
  abstract of a talk presented at "Perspectives in Numerical Analysis" (Helsinki, May 2008)
  and at the "7th Australia-New Zealand Mathematics Convention" (Christchurch, December 2008)
  
  
• Improving the stability of discrete least-squares method for membrane eigenvalue problems
  draft - P. Zitnan (Zilina, Slovakia)
  submitted (December 2008)
  
  
• Padua points: theory, computation and applications
  S. De Marchi
  slides of a Guest Lecture at the CMA (Center of Mathematics for Applications), University of Oslo (April 2009)
  
  
• Padua Points: Computational Aspects and some Applications
  S. De Marchi
  abstract of a talk presented at the Dept. of Mathematics, University of Hamburg (May 2009)
  
  
• A numerical code for fast interpolation and cubature at the Padua points
  M. Caliari (with S. De Marchi, A. Sommariva and M. Vianello)
  submitted to the Proceedings of the 9th CMMSE (Gijón, Spain, July 2009)
  
  
• On the Vandermonde Determinant of Padua-like Points
  L. Bos, S. De Marchi and S. Waldron
  published as "open problem" in Dolomites Research Notes on Approximation 2 (2009)
  
  
• Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave
  preprint - M. Caliari, S. De Marchi, A. Sommariva and M. Vianello
  Numer. Algorithms, to appear