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Errors of Approximation with Polynomial Splines of the Fifth Order

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Applied Physics, System Science and Computers II (APSAC 2017)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 489))

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Abstract

This paper is a continuation of a series of papers devoted to the construction and investigation of the properties of integro-differential polynomial splines of the fifth order. It is supposed that values of function in grid nodes and values of integrals over intervals are known. Solving the system of linear algebraic equations, we find basic splines. An approximation of the function in this paper is constructed on every grid interval separately using values of the function in two adjacent grid nodes and the values of three integrals over intervals, and basic splines.

We call this approximation an integro-differential spline and we call these basic splines integro-differential basic splines. The properties of interpolation with integro-differential polynomial basic splines are investigated. A comparison of the properties of integro-differential approximations for a different choice of integrals is presented. A comparison of the integro-differential approximation with approximation using polynomial splines of the Lagrangian type is made. Numerical examples are presented.

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Authors and Affiliations

  1. St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russia

    I. G. Burova & A. G. Doronina

Authors
  1. I. G. Burova
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  2. A. G. Doronina
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Corresponding author

Correspondence to I. G. Burova .

Editor information

Editors and Affiliations

  1. Department of Business Administration, University of West Attica, Athens, Greece

    Klimis Ntalianis

  2. Faculty of Mathematics, Al.I. Cuza University, Iasi, Romania

    Anca Croitoru

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Burova, I.G., Doronina, A.G. (2019). Errors of Approximation with Polynomial Splines of the Fifth Order. In: Ntalianis, K., Croitoru, A. (eds) Applied Physics, System Science and Computers II. APSAC 2017. Lecture Notes in Electrical Engineering, vol 489. Springer, Cham. https://doi.org/10.1007/978-3-319-75605-9_6

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  • DOI: https://doi.org/10.1007/978-3-319-75605-9_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-75604-2

  • Online ISBN: 978-3-319-75605-9

  • eBook Packages: EngineeringEngineering (R0)

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