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On Characterization of Poised Nodes for a Space of Bivariate Functions
Department of Informatics and Applied Mathematics, Yerevan State University, Yerevan, Armenia
Department of Informatics and Applied Mathematics, Yerevan State University, Yerevan, Armenia
- 1 Department of Informatics and Applied Mathematics, Yerevan State University, Yerevan, Armenia
- 2 Department of Informatics and Applied Mathematics, Yerevan State University, Yerevan, Armenia
Advances in Linear Algebra & Matrix Theory·Volume 06 (2016)·Pages 89–103·Published 28 November 2016·DOI10.4236/alamt.2016.64010
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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.
KeywordsBivariate Interpolation ProblemPoisednessFundamental FunctionBivariate Piecewise Linear FunctionReductions by Basic Subproblems
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