کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4638994 | 1632030 | 2014 | 10 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: On the singularity of multivariate Hermite interpolation On the singularity of multivariate Hermite interpolation](/preview/png/4638994.png)
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+km=d+k points in RdRd is singular if d≥2kd≥2k. And then we solve the Hermite interpolation problem on m≤d+3m≤d+3 nodes completely. Precisely, all Hermite interpolations of type total degree on m≤d+1m≤d+1 points with d≥2d≥2 are singular; only three cases for m=d+2m=d+2 and one case for m=d+3m=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.
Journal: Journal of Computational and Applied Mathematics - Volume 261, 1 May 2014, Pages 85–94