Approximation of functions by polynomials on an arbitrary interval using integral equations of Volterra

Halan  Vasyl Danylovych; Grod  Ivan Mykolayovych; Kravchuk Vasyl Rostislavovych

doi:https://doi.org/10.31861/bmj2018.03.036

Halan Vasyl Danylovych ¹ , Grod Ivan Mykolayovych ¹ , Kravchuk Vasyl Rostislavovych ¹

¹ Department of mathematics and methods of its teaching, Ternopil National Pedagogical University named after Volodymyr Hnatyuk, Ternopil, 46027, Ukraine

DOI: https://doi.org/10.31861/bmj2018.03.036

Keywords: approximation function, asymptotically best approximation, Volterra integral equations

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Abstract

The article describes algorithm for construction of polynomials for approximation of function on arbitrary interval from the range of its definition. It is shown that for the function $y=e^x$this algorithm allows us to construct polynomials of $n$-th degree, which make its asymptotically best approximation.

References

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ACS Style: Halan, .D.; Grod , I.M.; Kravchuk, V.R. Approximation of functions by polynomials on an arbitrary interval using integral equations of Volterra. Bukovinian Mathematical Journal. 2019, 6 https://doi.org/https://doi.org/10.31861/bmj2018.03.036
AMA Style: Halan D, Grod IM, Kravchuk VR. Approximation of functions by polynomials on an arbitrary interval using integral equations of Volterra. Bukovinian Mathematical Journal. 2019; 6(3-4). https://doi.org/https://doi.org/10.31861/bmj2018.03.036
Chicago/Turabian Style: Vasyl Danylovych Halan, Ivan Mykolayovych Grod , Vasyl Rostislavovych Kravchuk. 2019. "Approximation of functions by polynomials on an arbitrary interval using integral equations of Volterra". Bukovinian Mathematical Journal. 6 no. 3-4. https://doi.org/https://doi.org/10.31861/bmj2018.03.036

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