Cubic pencils of lines and bivariate interpolation

Authors:
J. M. Carnicer;M. Gasca
Affiliations:
University of Zaragoza, Spain;University of Zaragoza, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 2
Cited 0

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Geometric characterization and generalized principal lattices

Journal of Approximation Theory

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Abstract

Cubic pencils of lines are classified up to projectivities. Explicit formulae for the addition of lines on the set of nonsingular lines of the pencils are given. These formulae can be used for constructing planar generalized principal lattices, which are sets of points giving rise to simple Lagrange formulae in bivariate interpolation. Special attention is paid to the irreducible nonsingular case, where elliptic functions are used in order to express the addition in a natural form.