Abstract
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.
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Carnicer, J.M., Gasca, M., Sauer, T.: Interpolation lattices in several variables. Numer. Math. 102(4), 559–581 (2006)
Chung, K.C., Yao, T.H.: On lattices admitting unique Lagrange interpolations. SIAM J. Numer. Anal. 14(4), 735–743 (1977)
Coxeter, H.S.M.: Introduction to Geometry. Wiley Classics Library. Wiley, New York (1989)
Gasca, M., Sauer, T.: Polynomial interpolation in several variables. Adv. Comput. Math. 12(4), 377–410 (2000)
Lee, S.L., Phillips, G.M.: Construction of lattices for Lagrange interpolation in projective space. Constr. Approx. 7(3), 283–297 (1991)
Levy, H., Lessman, F.: Finite difference equations. Dover, New York (1992) (Reprint of the 1961 edition)
Phillips, G.M.: Interpolation and Approximation by Polynomials. CMS Books in Mathematics. Springer, Berlin Heidelberg New York (2003)
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Jaklič, G., Kozak, J., Krajnc, M. et al. Three-pencil lattices on triangulations. Numer Algor 45, 49–60 (2007). https://doi.org/10.1007/s11075-007-9068-4
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DOI: https://doi.org/10.1007/s11075-007-9068-4