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On multivariate interpolation. (English) Zbl 1145.41311

Summary: 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.

MSC:

41A63 Multidimensional problems
15B57 Hermitian, skew-Hermitian, and related matrices
30E05 Moment problems and interpolation problems in the complex plane
41A10 Approximation by polynomials

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