Bivariate Vector-Valued Osculatory Rational Interpolation Based on the Taylor Operator

JING Hui-qin

doi:10.3879/j.issn.1000-0887.2016.04.008

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JING Hui-qin. Bivariate Vector-Valued Osculatory Rational Interpolation Based on the Taylor Operator[J]. Applied Mathematics and Mechanics, 2016, 37(4): 404-415. doi: 10.3879/j.issn.1000-0887.2016.04.008

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Bivariate Vector-Valued Osculatory Rational Interpolation Based on the Taylor Operator

doi: 10.3879/j.issn.1000-0887.2016.04.008

JING Hui-qin

Adult Education College, Kunming University of Science and Technology, Kunming 650051, P.R.China

Received Date: 2015-11-16
Rev Recd Date: 2015-12-29
Publish Date: 2016-04-15

Abstract

Abstract

A new approach based on the Taylor operator was proposed for the bivariate vectorvalued osculatory rational interpolation. First, the rational interpolation basis functions of each order were defined by means of the known nodes. Second, a new type of interpolation operator similar to the Taylor formula for bivariate functions was established with the corresponding vector values and partial derivative values of each order. At last, the combined operations were carried out, and the explicit expressions of the bivariate vectorvalued osculatory rational interpolation functions of the 1st and 2nd orders were obtained. Naturally this approach was generalized to the kth order, and the error estimates were also made. The results of an example show that, this new approach is simple and formularized in calculation, and therefore potential for application.
- osculatory rational interpolation,
- bivariate vector,
- Taylor operator,
- basis function,
- interpolation function

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References(27)

References

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