Constructive approach to the monotone rearrangement of functions
| Autor: | Carlo Garoni, Giovanni Barbarino, Davide Bianchi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Pure mathematics
Sequence Bounded set Measurable function Continuous function Asymptotically uniform grids and quasi-uniform samples General Mathematics Quantile function Boundary (topology) 28A20 46E30 60E05 Numerical Analysis (math.NA) Monotone polygon Almost everywhere continuous functions Simple (abstract algebra) Settore MAT/05 FOS: Mathematics Almost everywhere Generalized inverse distribution function Uniform convergence Mathematics - Numerical Analysis Monotone rearrangement Mathematics |
| Popis: | We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost everywhere continuous function defined on a bounded set $\Omega$ with negligible boundary. Under additional assumptions on $f$ and $\Omega$, we prove that the convergence of the sequence is uniform. We also show that the same procedure applies to arbitrary measurable functions too, but with the substantial difference that in this case the procedure has only a theoretical interest and cannot be converted to an algorithm. Comment: In Press |
| Databáze: | OpenAIRE |
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