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TitleOn the singularity of multivariate Hermite interpolation
Author(s) Zhongxuan Luo, Zhaoliang Meng
TypeArticle in Journal
AbstractAbstract In this paper, we study the singularity of multivariate Hermite interpolation of type total degree. We present two methods to judge the singularity of the interpolation schemes considered and by methods to be developed, we show that all Hermite interpolation of type total degree on m = d + k points in R d is singular if d ≥ 2 k . And then we solve the Hermite interpolation problem on m ≤ d + 3 nodes completely. Precisely, all Hermite interpolations of type total degree on m ≤ d + 1 points with d ≥ 2 are singular; only three cases for m = d + 2 and one case for m = d + 3 can produce regular Hermite interpolation schemes, respectively. Besides, we also present a method to compute the interpolation space for Hermite interpolation of type total degree.
KeywordsHermite interpolation, Singularity, Interpolation space, Polynomial ideal
ISSN0377-0427
URL http://www.sciencedirect.com/science/article/pii/S037704271300602X
LanguageEnglish
JournalJournal of Computational and Applied Mathematics
Volume261
Number0
Pages85 - 94
Year2014
Edition0
Translation No
Refereed No
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