Constr Approx https://doi.org/10.1007/s00365-018-9433-7 Computing a Quantity of Interest from Observational Data 1 1 Ronald DeVore · Simon Foucart · 1 2,3 Guergana Petrova · Przemyslaw Wojtaszczyk Received: 13 June 2017 / Revised: 9 February 2018 / Accepted: 26 March 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract Scientiﬁc problems often feature observational data received in the form w = l ( f ),...,w = l ( f ) of known linear functionals applied to an unknown func- 1 1 m m tion f from some Banach space X , and it is required to either approximate f (the full approximation problem) or to estimate a quantity of interest Q( f ). In typical exam- ples, the quantities of interest can be the maximum/minimum of f or some averaged quantity such as the integral of f , while the observational data consists of point eval- uations. To obtain meaningful results about such problems, it is necessary to possess additional information about f , usually as an assumption that f belongs to a certain model class K contained in X . This is precisely the framework of optimal recovery, Communicated by Wolfgang Dahmen. This research was supported
Constructive Approximation – Springer Journals
Published: Jun 1, 2018
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