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Interflatation of Functions

In: Elements of the General Theory of Optimal Algorithms

Author

Listed:
  • Ivan V. Sergienko

    (National Academy of Sciences of Ukraine)

  • Valeriy K. Zadiraka

    (National Academy of Sciences)

  • Oleg M. Lytvyn

    (Ukrainian Engineering Pedagogics Academy)

Abstract

This chapter presents the operators of interflatation of functions of three variables on a system of mutually perpendicular planes using rational, polynomial, trigonometric auxiliary functions, and auxiliary functions in the form of splines. These operators use traces of the approximate function of three variables and traces of its normal derivatives on some system of planes. Note that the operators of interlineation and interflatation of functions are a natural generalization of the interpolation of functions of many variables. This chapter also presents possible applications of interlineation of functions in solving boundary value problems with partial derivatives within the framework of V.L. Rvachev’s structural method. This method is based on the use of R-functions that are positive in given domains, equal to zero at the boundary of domains that are negative outside these domains. The monograph presents three problems that can improve the computational properties of the structures of approximate solutions of boundary value problems, if to construct them use the interlineation operators of functions with automatic preservation of the class of differentiation. Here give integral representations of the residual terms of the approximation of differentiation functions of three variables.

Suggested Citation

  • Ivan V. Sergienko & Valeriy K. Zadiraka & Oleg M. Lytvyn, 2021. "Interflatation of Functions," Springer Optimization and Its Applications, in: Elements of the General Theory of Optimal Algorithms, chapter 0, pages 177-251, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-90908-6_4
    DOI: 10.1007/978-3-030-90908-6_4
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