WAM: Matlab package for multivariate polynomial fitting and interpolation on Weakly Admissible Meshes

Mesh constructors

planar meshes

Polygons
• wamquadrangle (WAM on a convex quadrangle or on a triangle)
• wampolygon (WAM on a general simple polygon)
  
  Domains related to circular arcs (sectors, lenses, lunes, ...)
• subpcheb (subperiodic Chebyshev-like angles)
• wamblend (WAM on an arc-blending region)
  
• wamblendplot (plots the region and the WAM)
  
• wamlune (WAM on a lune)
  
• wamluneplot (plots the lune and the WAM)
  
  Smooth convex domains
• convomesh (admissible mesh on a C^2 convex domain)

solid meshes

Cube
• wamlissa (WAM on Lissajous curves of the cube)
  
• lejacube30.txt (Discrete Leja Points of the cube up to degree 30 on a Lissajous curve)
  note: use the first (n+1)(n+2)(n+3)/6 to interpolate at degree n by wamfit.m below
  
  Cones and pyramids
• wamcone (WAM on a cone/pyramid by a 2d WAM of the base)
  

general tools

• chebpolys (computes the Chebyshev poynomials by recurrence)
  
• chebvand (Chebyshev-Vandermonde matrix, graded lexic. order)
  
• singlepts (eliminates multiple points)
  
• wamcomprex (WAM compression, under revision)
  

Polynomial fitting

• dexsets (extraction of discrete extremal sets of Fekete and Leja type from a WAM)
  
• wamdop (Discrete Orthogonal Polynomials on a WAM)
  
• wamdopeval (evaluation of DOPs)
  
• wamfit (polynomial fitting on a WAM; note: interpolates on discrete extremal sets)
  
• wamleb (Lebesgue constant of the fitting/interpolation operator)
  

Demos

planar meshes

• testf (user defined function)
  
• interpdemo (interpolation at discrete extremal sets)
  
• lsdemo (least-squares fitting)
  
• lebdemo (Lebesgue constants)
  

References

• see the web page: Weakly Admissible polynomial Meshes