Error at interpolation of some classes of functions by multilinear splines

V.F. Babenko; T.Yu. Leskevich

doi:10.15421/241004

Error at interpolation of some classes of functions by 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

We obtain the exact value of error at interpolation of some classes of multivariate functions, which are determined by given convex upwards majorant of modulus of continuity, by multilinear splines.

Keywords

multilinear function; modulus of continuity; interpolation

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References

Babenko V.F. "Interpolation of continuous maps by piecewise-linear ones", Matem. zametki, 1978; 24(1): pp. 43-50. (in Russian) doi:10.1007/BF01812980

Babenko V.F., Ligun A.A. "On interpolation by multifaceted functions", Matem. zametki, 1975; 18(6): pp. 803-814. (in Russian) doi:10.1007/BF01099983

Vakarchuk S.B. "On interpolation by bilinear splines", Matem. zametki, 1990; 47(5): pp. 26-40. (in Russian) doi:10.1007/BF01158084

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) doi:10.1007/s11253-005-0180-0

Korneichuk N.P. Exact constants in approximation theory, Nauka, Moscow, 1987; 424 p. (in Russian)

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

Storchai V.F. "The deviation of polygonal functions in the $$$L_p$$$ metric", Matem. zametki, 1969; 5(1): pp. 31-37. (in Russian) doi:10.1007/BF01098710

Storchai V.F. "Approximation of functions of two variables by polyhedral functions in the uniform metric", Izv. vuzov. Matematika, 1973; 8: pp. 84-88. (in Russian)

Shabozov M.Sh. "On error of interpolation by bilinear splines", Ukrainian Math. J., 1994; 46(11): pp. 1554-1560. (in Russian) doi:10.1007/BF01058889

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) doi:10.1007/BF02312471