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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Metric Approximation of Set-Valued Functions

## Metric Approximation of Set-Valued FunctionsAdd to your list(s) Download to your calendar using vCal - Elena Berdysheva (Justus-Liebig-Universität Gießen)
- Tuesday 12 March 2019, 15:00-16:30
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. ASC - Approximation, sampling and compression in data science We study approximation of set-valued functions (SVFs) | functions mapping a real interval to compact sets in Rd. In addition to the theoretical interest in this subject, it is relevant to various applications in elds where SVFs are used, such as economy, optimization, dynamical systems, control theory, game theory, dierential inclusions, geometric modeling. In particular, SVFs are relevant to the problem of the reconstruction of 3D objects from their parallel cross-sections. The images (values) of the related SVF are the cross-sections of the 3D object, and the graph of this SVF is the 3D object. Adaptations of classical sample-based approximation operators, in particular, of positive operators for approximation of SVFs with convex images were intensively studied by a number of authors. For example, R.A Vitale studied an adaptation of the classical Bernstein polynomial operator based on Minkowski linear combination of sets which converges to the convex hull of the image. Thus, the limit SVF is always a function with This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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