Unique solvability in bivariate Hermite interpolation

We consider the question of unique solvability in the context of bivariate Hermite interpolation. Starting from arbitrary nodes, we prescribe arbitrary conditions of Hermite type, and find an appropriate interpolation space in which the problem has a unique solution. We show that the coefficient mat...

Full description

Saved in:
Bibliographic Details
Published inElectronic transactions on numerical analysis Vol. 34; p. 20
Main Authors Marco, Ana, Ma
Format Journal Article
LanguageEnglish
Published Institute of Computational Mathematics 01.12.2008
Subjects
Interpolation
Matrices
Numerical analysis
Tensors (Mathematics)
Spain
Online AccessGet full text

Cover

More Information
Summary:We consider the question of unique solvability in the context of bivariate Hermite interpolation. Starting from arbitrary nodes, we prescribe arbitrary conditions of Hermite type, and find an appropriate interpolation space in which the problem has a unique solution. We show that the coefficient matrix of the associated linear system is a nonsingular submatrix of a generalized Kronecker product of nonsingular matrices corresponding to univariate Hermite interpolation problems. We also consider the case of generalized polynomials, such as Cauchy- Vandermonde systems. Key words. Hermite interpolation, bivariate interpolation, generalized Kronecker product. AMS subject classifications. 41A05, 41A63, 65D05
ISSN:1068-9613
1097-4067