# Linear versus Non-Linear Acquisition of Step-Functions

@article{Ettinger2007LinearVN, title={Linear versus Non-Linear Acquisition of Step-Functions}, author={Boris Ettinger and Niv Sarig and Yosef Yomdin}, journal={Journal of Geometric Analysis}, year={2007}, volume={18}, pages={369-399} }

We address in this article the following two closely related problems. 1. How to represent functions with singularities (up to a prescribed accuracy) in a compact way. 2. How to reconstruct such functions from a small number of measurements.The stress is on a comparison of linear and non-linear approaches. As a model case, we use piecewise-constant functions on [0,1], in particular, the Heaviside jump function ℋt=χ[0,t]. Considered as a curve in the Hilbert space L2([0,1]) it is completely…

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