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Approximation of functions by two-point Hermite interpolating polynomials

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Abstract

A polynomial approximating a given function is constructed assuming that the function and a certain set of its derivatives are known at the endpoints of a given interval. Various analytical formulas are derived for the approximating polynomial. An interpretation of the two-point approximation of the function is given and its relation to the Taylor series expansion of the function is indicated. A sufficient condition for the convergence of a sequence of two-point polynomials to a given function is established. Examples are given in which the sine function is approximated by a sequence of two-point Hermite polynomials on given intervals. The errors in the two-point and Taylor series approximations of the function are compared analytically and numerically.

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References

  1. L. D. Kudryavtsev, Calculus (Vysshaya Shkola, Moscow, 1970), Vol. 1 [in Russian].

  2. I. S. Berezin and N. P. Zhidkov, Computing Methods (Fizmatgiz, Moscow, 1962; Pergamon, Oxford, 1965), Vol. 1.

  3. I. B. Kozhukhov and A. A. Prokof’ev, Handbook of Mathematics (“List,” Moscow, 1999) [in Russian].

    Google Scholar 

  4. V. I. Goncharov, Theory of Interpolation and Approximation of Functions (Gostekhteorizdat, Moscow, 1934) [in Russian].

    Google Scholar 

  5. V. V. Prasolov, Polynomials (MTsNMO, Moscow, 1999) [in Russian].

    Google Scholar 

  6. E. A. Volkov, Numerical Methods (Fizmatgiz, Moscow, 1987) [in Russian].

    MATH  Google Scholar 

  7. I. P. Mysovskikh, Lectures on Computing Methods (Fizmatgiz, Moscow, 1962) [in Russian].

    Google Scholar 

  8. Mathematics and CAD 1 (Mir, Moscow, 1988) [in Russian].

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Authors and Affiliations

  1. State Research Institute of Aviation Systems, ul. Viktorenko 7, Moscow, 125319, Russia

    V. V. Shustov

Authors
  1. V. V. Shustov
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Correspondence to V. V. Shustov.

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Original Russian Text © V.V. Shustov, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 7, pp. 1091–1108.

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Shustov, V.V. Approximation of functions by two-point Hermite interpolating polynomials. Comput. Math. and Math. Phys. 55, 1077–1093 (2015). https://doi.org/10.1134/S0965542515040156

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  • DOI: https://doi.org/10.1134/S0965542515040156

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