Random Linear Operators Arising from Piecewise Linear Interpolation on the Unit Interval
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Fecha
2022-09-09
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Birkhäuser - Springer
Resumen
We introduce a sequence of random linear operators arising
from piecewise linear interpolation at a set of random nodes on the unit
interval. We show that such operators uniformly converge in probability
to the target function, providing at the same time rates of convergence.
Analogous results are shown for their deterministic counterparts, derived by taking expectations of the aforementioned random operators.
Special attention is paid to the case in which the random nodes are the
uniform order statistics, where an explicit form for their associated deterministic operators is provided. This allows us to compare the speed
of convergence of the aforementioned operators with that of the random
and deterministic Bernstein polynomials
Descripción
Palabras clave
Random linear operator, Uniform convergence in probability, Ditzian–Totik modulus of smoothness, Uniform order statistics, Rate of convergence, Confidence band
Citación
Adell, J.A., Cárdenas-Morales, D. Random Linear Operators Arising from Piecewise Linear Interpolation on the Unit Interval. Mediterr. J. Math. 19, 223 (2022)