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The proper interpolation space for multivariate Birkhoff interpolation

โœ Scribed by Junjie Chai; Na Lei; Ying Li; Peng Xia

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
236 KB
Volume
235
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

Multivariate Birkhoff interpolation problem has many important applications, such as in finite element method. In this paper two algorithms are given to compute the basis of the minimal interpolation space and the lower interpolation space respectively for an arbitrary given node set and the corresponding interpolation conditions on each node. We can get the monomial basis, Newton-type basis as well as Lagrange-type basis. The interpolation polynomial can be derived from the basis directly.

๐Ÿ“œ SIMILAR VOLUMES

Applying Quantifier Elimination to the B
Applying Quantifier Elimination to the Birkhoff Interpolation Problem
โœ LAUREANO GONZALEZ-VEGA ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 706 KB

This paper is devoted to show how to use Computer Algebra and Quantifier Elimination to solve some particular instances of the Birkhoff Interpolation Problem. In particular, this problem is completely solved for degree smaller or equal than 3 and any number of nodes and several instances of degree 4