Journal article
Approximation of functions of several variables by continuous linear splines on rectilinear grids?
Authors list: Berdysheva, E. E.; Mehmonzoda, S. N.; Shabozov, M. Sh.
Publication year: 2021
Pages: 1-23
Journal: Jaén journal on approximation
Volume number: 12
ISSN: 1889-3066
eISSN: 1989-7251
Publisher: Universidad de Jaén
Abstract:
We consider approximation of functions of several variables by continuous linear splines interpolating the given function in the knots of a rectilinear lattice. For function classes defined in terms of a modulus of continuity, we give an exact es-timate for the error of approximation. In the particular case when the modulus of continuity is concave and the distance between points in Rd is measured in the l(p)-norm with 1 <= P <= 3, we calculate an explicit value of the exact approximation error on the class. Surprisingly, the behavior changes dramatically if P > 3. We show that the our estimate is no longer true, in general, when P > 3. We also consider approximation of a first derivative of a function by the corre-sponding derivative of the linear continuous spline and obtain an upper estimate for the error of approximation for an arbitrary modulus of continuity, all 1 <= P <= infinity, and triangulations of the staircase type.
Citation Styles
Harvard Citation style: Berdysheva, E., Mehmonzoda, S. and Shabozov, M. (2021) Approximation of functions of several variables by continuous linear splines on rectilinear grids?, JAEN JOURNAL ON APPROXIMATION, 12, pp. 1-23
APA Citation style: Berdysheva, E., Mehmonzoda, S., & Shabozov, M. (2021). Approximation of functions of several variables by continuous linear splines on rectilinear grids?. JAEN JOURNAL ON APPROXIMATION. 12, 1-23.
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