Lagrange interpolation set along linear piecewise algebraic curves

This paper discusses the Lagrange interpolation problem in continuous bivariate spline spaces over regular triangulations. By using the so-called Lagrange interpolation set along piecewise algebraic curves, we develop a new approach of constructing the interpolation set for continuous spline spaces. We show the property of this set on star region, and construct the interpo- lation set for continuous bivariate spline spaces over arbitrary triangulations. The construction only depends on the number of points on the piecewise algebraic curve in each cell.

Keywords

Bivariate spline; Lagrange interpolation set; linear piecewise algebraic curve; interpolation set along piecewise algebraic curves

2010 Mathematics Subject Classification

41A05, 41A15, 41A63, 65D05, 65D07

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Published 1 January 2009