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Taylor type and Hermite type interpolants in \(\mathbb {R}^{n}\)

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Abstract

We construct new polynomial interpolation schemes of Taylor and Hermite types in \(\mathbb {R}^{n}\). The interpolation conditions are real parts and imaginary parts of certain differential operators. We also give formulas for the interpolation polynomials which are of Newton form and can be computed by an algorithm.

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Acknowledgements

We are grateful to anonymous referees for their constructive comments. A part of this work was done when the first author was working at Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the VIASM for providing a fruitful research environment and working condition.

Funding

This research is funded by the Vietnam Ministry of Education and Training under grant number B2021-SPH-16.

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Correspondence to Phung Van Manh.

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Van Manh, P., Van Trao, N., Tung, P.T. et al. Taylor type and Hermite type interpolants in \(\mathbb {R}^{n}\). Numer Algor 89, 145–166 (2022). https://doi.org/10.1007/s11075-021-01109-6

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  • DOI: https://doi.org/10.1007/s11075-021-01109-6

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