Add to ORKGContribution to "School (and Workshop) on Computational Algebra for Algebraic Geometry and Statistics", Torino, September 2004. Summary. -A generalised (multivariate) divided difference formula is given for an arbitrary finite set of points with no subsets of three points that lie on a line. This follows from an extension of the Newton's polynomials and Newton's interpolation formula. It is derived as the interpolation based on Gröbner bases for the grid expressed as a zero-dimensional variety and is typically dependent on the chosen term-ordering and the selected ordering of points in the grid
The generalization of Lagrange and Newton univariate interpolation formulae is one of the topics of ...
AbstractLet a polynomial of degree n be given by its values at n+1 general points. Consider the prob...
Abstract. In this paper we prove that the existence of an error for-mula of a form suggested in [2] ...
Gr\uf6bner bases are used in experimental design and interpolation. They provide a special way to wr...
In this paper, the importance of the choice of monomial ordering is emphasized. Moreover, an algorit...
In this paper we establish the unisolvence of any interlacing pair of rectangular grids of points wi...
AbstractWe present formulas for the divided differences of the remainder of the interpolation polyno...
Two-variable interpolation by polynomials is investigated for the given f : R2 ! R. The new idea is ...
AbstractThis note describes ideals generated by symmetric polynomials in two sets of variables A,B. ...
Abstract. Under general conditions, the equation g(x1,..., xq, y) = 0 implicitly defines y locally ...
AbstractWe generalize the univariate divided difference to a multivariate setting by considering lin...
AbstractIn this paper we study multivariate polynomial interpolation on Aitken–Neville sets by relat...
In this thesis, we study the basis sets of pure difference ideals, that is, ideals that are generate...
In this paper we present a new kind of algorithm, for finding a solution (g0 (x), g1 (x), . . . , gn...
Abstract. The construction of a polynomial interpolant to data given at finite pointsets in 1R "...
The generalization of Lagrange and Newton univariate interpolation formulae is one of the topics of ...
AbstractLet a polynomial of degree n be given by its values at n+1 general points. Consider the prob...
Abstract. In this paper we prove that the existence of an error for-mula of a form suggested in [2] ...
Gr\uf6bner bases are used in experimental design and interpolation. They provide a special way to wr...
In this paper, the importance of the choice of monomial ordering is emphasized. Moreover, an algorit...
In this paper we establish the unisolvence of any interlacing pair of rectangular grids of points wi...
AbstractWe present formulas for the divided differences of the remainder of the interpolation polyno...
Two-variable interpolation by polynomials is investigated for the given f : R2 ! R. The new idea is ...
AbstractThis note describes ideals generated by symmetric polynomials in two sets of variables A,B. ...
Abstract. Under general conditions, the equation g(x1,..., xq, y) = 0 implicitly defines y locally ...
AbstractWe generalize the univariate divided difference to a multivariate setting by considering lin...
AbstractIn this paper we study multivariate polynomial interpolation on Aitken–Neville sets by relat...
In this thesis, we study the basis sets of pure difference ideals, that is, ideals that are generate...
In this paper we present a new kind of algorithm, for finding a solution (g0 (x), g1 (x), . . . , gn...
Abstract. The construction of a polynomial interpolant to data given at finite pointsets in 1R "...
The generalization of Lagrange and Newton univariate interpolation formulae is one of the topics of ...
AbstractLet a polynomial of degree n be given by its values at n+1 general points. Consider the prob...
Abstract. In this paper we prove that the existence of an error for-mula of a form suggested in [2] ...