SOFTWARE produced by the CAA group

Multivariate interpolation and quadrature

(at MARCO CALIARI's web site)

Bivariate polynomial interpolation and hyperinterpolation (the PADUA POINTS codes are here)


• HyperCube (Fortran 77 code for hyperinterpolation in the cube)
  by M. Caliari, S. De Marchi and M. Vianello (see paper)
  
• Padua2D (Fortran 77 code for interpolation at Padua-like points on rectangles, triangles and ellipses); the code is also in the Netlib
  by M. Caliari, S. De Marchi and M. Vianello (see paper) - ACM Trans. Math. Software 35-3 (2008)
  a variant has been used in Fun2D of the CP2K simulation package for molecular dynamics (see paper)
• Padua2DM (a Matlab/Octave code for interpolation and cubature at the Padua points); the code is also in the Netlib
  by M. Caliari, S. De Marchi, A. Sommariva and M. Vianello (see paper) - Numer. Algorithms 56 (2011)
  
• XuPad2D (Matlab interface for hyperinterpolation at Xu points and interpolation at Padua points on rectangles)
  by M. Caliari, S. De Marchi, R. Montagna and M. Vianello, replaces the former interface Hyper2D (see paper)
  

(at STEFANO DE MARCHI's web site)

Trivariate polynomial interpolation and hyperinterpolation


• Hyper3 (Matlab code for cubature and hyperinterpolation in the 3-cube)
  by S. De Marchi and M. Vianello (see paper)
  
• 3dWAM (Matlab functions to compute weakly admissible meshes of 3-dimensional cones and solids of rotation)
  by S. De Marchi and M. Vianello (see paper)
  

(at ALVISE SOMMARIVA's web site)

Extremal sets for bivariate polynomial interpolation


• InterpSets (bivariate Lebesgue and Fekete interpolation sets)
  by M. Briani, A. Sommariva and M. Vianello (see paper)
  
• Polygint (Matlab code for polynomial interpolation and cubature at Discrete Extremal Sets of polygons: preliminary nonoptimized version)
  by M. Gentile, A. Sommariva and M. Vianello (see paper)
  
  Algebraic cubature over polygons and over complex geometries
  
  
• ChebfunGauss (Matlab code for Gauss-Green cubature by the Chebfun package)
  by A. Sommariva and M. Vianello (see paper)
  
• PolyGauss (Matlab code for product Gauss cubature over polygons)
  by A. Sommariva and M. Vianello (see paper); see also Polygint above
  
• SplineGauss (Matlab code for Gauss-Green cubature over spline curvilinear polygons)
  by A. Sommariva and M. Vianello (see paper)
  
  Meshless cubature
  
  
• GreenDisk (Matlab code for meshless cubature over disks and annular sectors by Thin-Plate Splines and Green's formula)
  by A. Punzi, A. Sommariva and M. Vianello (see paper)
  

(at MARCO VIANELLO's web site)

Multivariate polynomial approximation


• approxfek (Matlab function to compute approximate Fekete and Leja points from a 2d or 3d mesh/cloud - version 1.2)
  by A. Sommariva and M. Vianello (see paper)
  
• convomesh (Matlab function to compute optimal polynomial meshes on planar C^2 convex domains - version 1.0)
  by F. Piazzon and M. Vianello (see paper)
  
  Subperiodic trigonometric quadrature
  
  
• trigauss (Matlab function for subperiodic trigonometric Gaussian quadrature - version 1.1; see here for version 1.0)
  by G. Da Fies, A. Sommariva and M. Vianello (see paper)
  note: part of the code (version 1.0) has been used for comparison by Walter Gautschi in his SRJAC repository for sub-range Jacobi polynomials
  
• trigquad (Matlab function for subperiodic trigonometric quadrature - version 1.1; see here for version 1.0)
  by G. Da Fies and M. Vianello (see paper)
  
  Product Gaussian quadrature on circular/elliptical sections
  
  
• gqcircsect, gqcircsegm, gqcirczone, gqsymmlens (Matlab functions for product Gaussian quadrature on disk sections:
  circular sectors, segments, zones, symmetric lenses - version 1.0)
  by G. Da Fies and M. Vianello (see paper)
  
• gqdbubble, gqlens, gqlune (Matlab functions for product Gaussian quadrature on regions generated by two arbitrary overlapping disks:
  double bubbles (union), lenses (intersection), lunes (difference) - version 1.0)
  by G. Da Fies and M. Vianello (see paper1 and paper2)
  
• gqellblend (Matlab function for product Gaussian quadrature by linear blending of elliptical arcs - version 1.0)
  by G. Da Fies, A. Sommariva and M. Vianello (see paper)