@manuascript {31886,
	title = {Robust Faber--Schauder approximation based on discrete observations of an antiderivative},
	journal = {Mathematics of Operations Research},
	year = {Accepted},
	abstract = {We study the problem of reconstructing the Faber--Schauder coefficients of a continuous function\&nbsp;f\&nbsp;from discrete observations of its antiderivative\&nbsp;F. Our approach starts with formulating this problem through piecewise quadratic spline interpolation. We then provide a closed-form solution and an in-depth error analysis. These results lead to some surprising observations, which also throw new light on the classical topic of quadratic spline interpolation itself: They show that the well-known instabilities of this method can be located exclusively within the final generation of estimated Faber--Schauder coefficients, which suffer from non-locality and strong dependence on the initial value and the given data. By contrast, all other Faber--Schauder coefficients depend only locally on the data, are independent of the initial value, and admit uniform error bounds. We thus conclude that a robust and well-behaved estimator for our problem can be obtained by simply dropping the final-generation coefficients from the estimated Faber--Schauder coefficients.},
	url = {https://arxiv.org/pdf/2211.11907.pdf},
	author = {Xiyue Han and Alexander Schied}
}
