论文信息 - On non-existence of certain error formulas for ideal interpolation

On non-existence of certain error formulas for ideal interpolation

We answer a question raised by Carl de Boor regarding the existence of certain ''good'' error formulas for ideal interpolation. We will show that, for a specific form of ideal interpolation by linear polynomials in two variables, such formulas do not exist.

Boris Shekhtman | B. Shekhtman

[1] B. Shekhtman. Ideal Interpolation: Translations to and from Algebraic Geometry , 2009 .

[2] S. Waldron. The Error in Linear Interpolation at the Vertices of a Simplex , 1998 .

[3] Amos Ron,et al. On polynomial ideals of finite codimension with applications to box spline theory , 1991 .

[4] Boris Shekhtman,et al. On the Näıve Error Formula for Bivariate Linear Interpolation , 2005 .

[5] C. D. Boor. On the error in multivariate polynomial interpolation , 1992 .

[6] Boris Shekhtman,et al. On one Question of Ed Sa ¤ , 2006 .

[7] David A. Cox,et al. Ideals, Varieties, and Algorithms , 1997 .

[8] G. Alexits. Approximation theory , 1983 .

[9] L. Schumaker,et al. Surface Fitting and Multiresolution Methods , 1997 .

[10] B. Shekhtman. On Error Formulas for Multivariate Polynomial Interpolation , 2007 .

[11] Larry L. Schumaker,et al. Approximation theory XI : Gatlinburg 2004 , 2005 .

[12] C. D. Boor. The Error in Polynomial Tensor-Product, and Chung-Yao, Interpolation , 2009 .