# On Multivariate Interpolation

@article{Olver2006OnMI, title={On Multivariate Interpolation}, author={Peter J. Olver}, journal={Studies in Applied Mathematics}, year={2006}, volume={116} }

A new approach to interpolation theory for functions of several variables is proposed. We develop a multivariate divided difference calculus based on the theory of noncommutative quasi‐determinants. In addition, intriguing explicit formulae that connect the classical finite difference interpolation coefficients for univariate curves with multivariate interpolation coefficients for higher dimensional submanifolds are established.

## 121 Citations

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We find geometric and arithmetic conditions on a finite set of integer exponents and the characteristic of a field k in order to characterize the irreducibility of the determinant of the generic…

### Christoffel transformations for multivariate orthogonal polynomials

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We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topology and algebraic…

### Geometric Integration via Multi-space

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The method of invariantization is based on the equivariant moving frame theory applied to prolonged symmetry group actions on multi-space, which has been proposed as the proper geometric setting for numerical analysis.

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