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Random Linear Operators Arising from Piecewise Linear Interpolation on the Unit Interval

Fecha

2022-09-09

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Editor

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)

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