The error at interpolation of some classes of multivariable functions by multifaceted functions and multilinear splines

V.F. Babenko (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0001-6677-1914
T.Yu. Leskevich (Oles Honchar Dnipropetrovsk National University)

Abstract


For functions defined on $$$n$$$-dimensional parallelepiped from classes determined by given upwards full module of continuity, the exact value of error of interpolation by multifaceted functions and multilinear splines is obtained.

Keywords


multifaceted function; multilinear function; spline; error; interpolation; full module of continuity

References


Malozemov V.N. "On deviation of broken lines", Vestnik LGU, 1966; 7: pp. 150-153. (in Russian)

Storchai V.F. "Approximation of continuous two-variable functions by multifaceted functions and spline-functions in uniform metric", Researches on modern problems of summation and approximation of functions and their applications, Dnipropetrovsk, 1975; pp. 82-89. (in Russian)

Babenko V.F., Ligun A.A. "On interpolation by multifaceted functions", Matem. zametki, 1975; 18(6): pp. 803-814. (in Russian)

Babenko V.F. "Interpolation of continuous maps by piecewise-linear ones", Matem. zametki, 1978; 24(1): pp. 43-50. (in Russian)

Vakarchuk S.B. "On interpolation by bilinear splines", Matem. zametki, 1990; 47(5): pp. 26-40. (in Russian)

Shabozov M.Sh. "On error of interpolation by bilinear splines", Ukrainian Math. J., 1994; 46(11): pp. 1554-1560. (in Russian)

Shabozov M.Sh. "Exact estimates of simultaneous approximation of two-variable functions and their derivatives by bilinear splines", Mat. zametki, 1996; 59(1): pp. 142-152. (in Russian)

Vakarchuk S.B., Myskin K.Yu. "Some problems of simultaneous approximation of two-variable functions and their derivatives by interpolation bilinear splines", Ukrainian Math. J., 2005; 57(2): pp. 147-157. (in Russian)

Babenko V.F., Leskevich T.Yu. "The error at interpolation of some classes of functions by multilinear splines", Dnipr. Univ. Math. Bull., 2010; 18(6/1): pp. 28-37. (in Russian)




DOI: https://dx.doi.org/10.15421/241206

  

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Copyright (c) 2012 V.F. Babenko, T.Yu. Leskevich

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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