Open AccessOperator interpolation formulas of Hermitе type with arbitrary multiplicity nodes based on identity transformations of function
Author(s) -
Марина Викторовна Игнатенко
Publication year - 2018
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2018-54-3-263-272
Subject(s) - mathematics , birkhoff interpolation , trigonometric interpolation , interpolation (computer graphics) , mathematical analysis , spline interpolation , hypergeometric function , hermite interpolation , linear interpolation , hermite polynomials , polynomial interpolation , algebra over a field , pure mathematics , bilinear interpolation , polynomial , frame (networking) , telecommunications , statistics , computer science
The problem of construction and research of Hermite interpolation formulas with nodes of arbitrary multiplicity for operators given in functional spaces of one and two variables is considered. The construction of operator interpolation polynomials is based both on interpolation polynomials for scalar functions with respect to an arbitrary Chebyshev system and on identity transformations of functions. The reduced operator formulas contain the Stieltjes integrals and the Gateaux differentials of an interpolated operator and are invariant for a special class of operator polynomials of appropriate degree. For some of the obtained operator polynomials, an explicit representation of the interpolation error is found. Particular cases of Hermite formulas based both on the integral transformations of Hankel, Abel, Fourier and on the Fourier sine (cosine) transform are considered. The application of separate interpolation formulas is illustrated by examples. The presented results can be used in theoretical research as the basis for construction of approximate methods for solving integral, differential and other types of nonlinear operator equations.