Spaces of generalized splines over T-meshes

• Cesare Bracco ^[1] ; Fabio Roman ^[2]
  1. [1] University of Florence

     University of Florence

     Firenze, Italia

     
  2. [2] University of Turin

     University of Turin

     Torino, Italia

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 294, Nº 1 (1 March 2016), 2016, págs. 102-123
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.08.006
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• Resumen

  • We consider a class of non-polynomial spaces, namely a noteworthy case of Extended Chebyshev spaces, and we generalize the concept of polynomial spline space over T-mesh to this non-polynomial setting: in other words, we focus on a class of spaces spanned, in each cell of the T-mesh, both by polynomial and by suitably-chosen non-polynomial functions, which we will refer to as generalized splines over T-meshes. For such spaces, we provide, under certain conditions on the regularity of the space, a study of the dimension and of the basis, based on the notion of minimal determining set, as well as some results about the dimension of refined and merged T-meshes. Finally, we study the approximation power of the just constructed spline spaces.