1. Three-pencil lattice on triangulationsGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2007, objavljeni znanstveni prispevek na konferenci Opis: In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries over to triangulations in a natural way. The construction is based upon group action of S 3 on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.
Ključne besede: numerical analysis, lattice, barycentric coordinates, triangulations, interpolation
Objavljeno v RUP: 03.04.2017; Ogledov: 2123; Prenosov: 84
 Povezava na celotno besedilo |
2. Barycentric coordinates for Lagrange interpolation over lattices on a simplexGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2008, objavljeni znanstveni prispevek na konferenci Opis: In this paper, a ▫$(d+1)$▫-pencil lattice on a simplex in ▫${\mathbb{R}}^d$▫ is studied. The lattice points are explicitly given in barycentric coordinates. This enables the construction and the efficient evaluation of the Lagrange interpolating polynomial over a lattice on a simplex. Also, the barycentric representation, based on shape parameters, turns out to be appropriate for the lattice extension from a simplex to a simplicial partition.
Ključne besede: numerical analysis, lattice, barycentric coordinates, simplex, interpolation
Objavljeno v RUP: 03.04.2017; Ogledov: 2237; Prenosov: 139
Povezava na celotno besedilo |
3. Lattices on simplicial partitionsGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2010, objavljeni znanstveni prispevek na konferenci Opis: In this paper, a ▫$(d+1)$▫-pencil lattices on a simplex in ▫${\mathbb{R}}^d$▫ are studied. The barycentric approach naturally extends the lattice from a simplex to a simplicial partition, providing a continuous piecewise polynomial interpolant over the extended lattice. The number of degrees of freedom is equal to the number of vertices of the simplicial partition. The constructive proof of thisfact leads to an efficient computer algorithm for the design of a lattice.
Ključne besede: numerical analysis, lattice, barycentric coordinates, simplicial partition
Objavljeno v RUP: 03.04.2017; Ogledov: 2146; Prenosov: 135
Povezava na celotno besedilo |
