Piecewise Bivariate Hermite Interpolations for Large Sets of Scattered Data
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-04-08
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
The requirements for interpolation of scattered data are high accuracy and high efficiency.
In this paper, a piecewise bivariate Hermite interpolant satisfying these requirements is proposed.
We firstly construct a triangulation mesh using the given scattered point set.
Based on this mesh, the computational point (x,y) is divided into two types: interior point and exterior point.
The value of Hermite interpolation polynomial on a triangle will be used as the approximate value if point (x,y) is an interior point, while the value of a Hermite interpolation function with the form of weighted combination will be used if it is an exterior point.
Hermite interpolation needs the first-order derivatives of the interpolated function which is not directly given in scatted data, so this paper also gives the approximate derivative at every scatted point using local radial basis function interpolation.
And numerical tests indicate that the proposed piecewise bivariate Hermite interpolations are economic and have good approximation capacity.
American Psychological Association (APA)
Feng, Renzhong& Zhang, Yanan. 2013. Piecewise Bivariate Hermite Interpolations for Large Sets of Scattered Data. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-456484
Modern Language Association (MLA)
Feng, Renzhong& Zhang, Yanan. Piecewise Bivariate Hermite Interpolations for Large Sets of Scattered Data. Journal of Applied Mathematics No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-456484
American Medical Association (AMA)
Feng, Renzhong& Zhang, Yanan. Piecewise Bivariate Hermite Interpolations for Large Sets of Scattered Data. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-456484
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-456484