Bojanov, B.D., Hakopian, H. and Sahakian, A. (1993) Spline Functions and Multivariate Interpolations, Mathematics and Its Applications. Vol. 248, Kluwer Acad. Publishers Group, Dordrecht.

has been cited by the following article:

• TITLE: On Characterization of Poised Nodes for a Space of Bivariate Functions

  AUTHORS: Hayk Avdalyan, Hakop Hakopian

  KEYWORDS: Bivariate Interpolation Problem, Poisedness, Fundamental Function, Bivariate Piecewise Linear Function, Reductions by Basic Subproblems

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.6 No.4, November 28, 2016

  ABSTRACT: There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials, or spline functions the mentioned results are well-known. In contrast with this, there are no such results in the bivariate case. As an exception, one may consider only the Pascal classic theorem, in the interpolation theory interpretation. In this paper, we consider a space of bivariate piecewise linear functions, for which we can readily find out whether the given node set is poised or not. The main tool we use for this purpose is the reduction by a basic subproblem, introduced in this paper.