High Order Derivative Rational Interpolation Algorithm With Heredity

JING Ke; LIU Ye-zheng; KANG Ning

doi:10.3879/j.issn.1000-0887.2014.08.009

Volume 35 Issue 8

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JING Ke, LIU Ye-zheng, KANG Ning. High Order Derivative Rational Interpolation Algorithm With Heredity[J]. Applied Mathematics and Mechanics, 2014, 35(8): 913-919. doi: 10.3879/j.issn.1000-0887.2014.08.009

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High Order Derivative Rational Interpolation Algorithm With Heredity

doi: 10.3879/j.issn.1000-0887.2014.08.009

¹School of Management, Hefei University of Technology, Hefei 230009, P.R.China;²School of Mathematics and Finance, Fuyang Teachers College, Fuyang, Anhui 236037, 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)（2013CB329603）

Received Date: 2013-12-06
Rev Recd Date: 2014-06-09
Publish Date: 2014-08-15

Abstract

Abstract

Osculatory rational interpolation was an important theme of function approximation, meanwhile, reducing the degree and solving the existence of the osculatory rational interpolation function made a crucial problem for rational interpolation. The previous algorithms of osculatory rational interpolation functions mostly depended on the continued fraction with conditional feasibility and high computation complexity. Based on heredity of the Newton interpolation and the method of piecewise combination, an osculatory rational interpolation function without real poles was constructed to meet the condition of high order derivative interpolation, and was in turn extended to the vector-valued cases. It not only solved the existence problem for the osculatory rational interpolation function, but reduced the degree of the rational function. Furthermore, the error estimates of the new algorithm was given. Results of the numerical examples illustrate the new algorithm’s heredity, low computation complexity and easy programmability.
- osculatory rational interpolation,
- Newton interpolation,
- piecewise combination,
- heredity,
- high order derivative

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References(14)

References

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