Multivariate divided differences and multivariate interpolation of Lagrange and Hermite type
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TL;DR: In this article, the authors give a natural definition of multivariate divided differences and construct the multivariate analog of Lagrange interpolation, and give a multivariate representation of a function f in terms of the above mentioned polynomials and divided differences.
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About: This article is published in Journal of Approximation Theory. The article was published on 01 Mar 1982. and is currently open access. The article focuses on the topics: Hermite interpolation & Multivariate interpolation.
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Citations
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Multivariate spline spaces
Charles K. Chui,Ren-Hong Wang +1 more
TL;DR: In this article, all of the properties and applications of multivariate spline functions can be derived from the basic theories in Chapter 1, and the expressions of the multi-branch functions in §2 of Chapter 1 are inconvenient to be applied directly because the expressions also rely on the solutions of the global conformality conditions so as to determine all the smooth cofactors.
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•Proceedings Article
What is the natural generalization of univariate splines to higher dimensions
Marian Neamtu
- 01 Jan 2001
TL;DR: In this article, the problem of defining multivariate splines in a natural way is formulated and discussed, and several existing constructions of multiivariate spline are surveyed, namely those based on simplex splines, and various difficulties and practical limitations associated with such constructions are pointed out.
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References
On Multivariate B-Splines
TL;DR: In this article, a multivariate B-spline is constructed in terms of certain multivariate "fundamental solutions" which are analogous to the usual univariate truncated powers.
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On a numerically efficient method for computing multivariate B-splines
Charles A. Micchelli
- 01 Jan 1979
TL;DR: In this article, an algorithm for the computation of smooth piecewise polynomials (multivariate B-spline) is given, and the results of numerical calculation for twelve typical B-Spline are given.