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论文类型：期刊论文

发表时间：2014-05-01

发表刊物：JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

收录刊物：SCIE、EI

卷号：261

页面范围：85-94

ISSN号：0377-0427

关键字：Hermite interpolation; Singularity; Interpolation space; Polynomial ideal

摘要：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 >= 2k. 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. (C) 2013 Elsevier B.V. All rights reserved.