Bivariate Osculatory Rational Interpolation on Rectangular Grids

JING Ke; KANG Ning

doi:10.3879/j.issn.1000-0887.2015.06.010

Volume 36 Issue 6

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JING Ke, KANG Ning. Bivariate Osculatory Rational Interpolation on Rectangular Grids[J]. Applied Mathematics and Mechanics, 2015, 36(6): 659-667. doi: 10.3879/j.issn.1000-0887.2015.06.010

Citation:

JING Ke, KANG Ning. Bivariate Osculatory Rational Interpolation on Rectangular Grids[J]. Applied Mathematics and Mechanics, 2015, 36(6): 659-667. doi: 10.3879/j.issn.1000-0887.2015.06.010

Citation:

JING Ke, KANG Ning. Bivariate Osculatory Rational Interpolation on Rectangular Grids[J]. Applied Mathematics and Mechanics, 2015, 36(6): 659-667. doi: 10.3879/j.issn.1000-0887.2015.06.010

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Bivariate Osculatory Rational Interpolation on Rectangular Grids

doi: 10.3879/j.issn.1000-0887.2015.06.010

JING Ke^1,2,
KANG Ning³

¹School of Mathematics and Finance, Fuyang Teachers College, Fuyang, Anhui 236037, P.R.China;²School of Management, Hefei University of Technology, Hefei 230009, P.R.China;³School of Economics and Management, Fuyang Teachers College, Fuyang, Anhui 236037, P.R.China

Funds: The National Basic Research Program of China (973 Program)（2013CB329600）;The National Natural Science Foundation of China（71371062）

Received Date: 2014-09-09
Rev Recd Date: 2014-10-13
Publish Date: 2015-06-15

Abstract

Abstract

The bivariate osculatory rational interpolation is an important element of rational interpolation, and reducing the degrees of the osculatory rational interpolation functions and solving their existence make an important problem. The bivariate osculatory rational interpolation algorithms mostly have conditional feasibility and massive computational complexity with high function degrees. A bivariate osculatory rational interpolation algorithm was obtained on rectangular grids and extended to vector-valued cases, with the method of bivariate Hermite interpolation basis function in view of the error characteristics of bivariate polynomial interpolation. The numerical examples illustrate that, compared to other methods, the feasibility of the presented algorithm is unconditional, the degrees of the related rational functions are lower, and the algorithm has less computational complexity.
- bivariate osculatory rational interpolation,
- error formula,
- bivariate Hermite interpolation,
- basis function

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References(16)

References

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