{"product_id":"9781783263042","title":"Approximation Of Set-valued Functions: Adaptation Of Classical Approximation Operators: Adaptation of Classical Approximation Operators","description":"\u003cp\u003eThis book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previous results on this topic are mainly confined to the convex case. The approach taken in this book is to adapt classical approximation operators and to provide error estimates in terms of the regularity properties of the approximated set-valued functions. Specialized results are given for functions with 1D sets as values.\u003c\/p\u003e\u003cb\u003eContents:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eScientific Background:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eOn Functions with Values in Metric Spaces\u003c\/li\u003e\n\u003cli\u003eOn Sets\u003c\/li\u003e\n\u003cli\u003eOn Set-Valued Functions (SVFs)\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eApproximation of SVFs with Images in ℝ\u003csup\u003en\u003c\/sup\u003e:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eMethods Based on Canonical Representations\u003c\/li\u003e\n\u003cli\u003eMethods Based on Minkowski Convex Combinations\u003c\/li\u003e\n\u003cli\u003eMethods Based on the Metric Average\u003c\/li\u003e\n\u003cli\u003eMethods Based on Metric Linear Combinations\u003c\/li\u003e\n\u003cli\u003eMethods Based on Metric Selections\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eApproximation of SVFs with Images in ℝ:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eSVFs with Images in ℝ \u003c\/li\u003e\n\u003cli\u003eMulti-Segmental and Topological Representations\u003c\/li\u003e\n\u003cli\u003eMethods Based on Topological Representation\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cb\u003eReadership:\u003c\/b\u003e Researchers and graduate students in the fields of approximation theory, set-valued analysis, dynamical systems, control and game theory, optimization and geometric modeling.\u003cbr\u003e\u003cb\u003eKey Features:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eThis is the only book on the subject of approximation of set-valued functions\u003c\/li\u003e\n\u003cli\u003eIt presents the pioneering work on the approximation of set-valued functions with general (not necessarily convex) sets as values\u003c\/li\u003e\n\u003cli\u003eThe first author is an internationally known expert in the field of Approximation Theory, the second author is an expert in numerical set-valued and non-smooth analysis. The third author received her PhD recently under the supervision of the first two authors. Many of the results presented in the book are based on her thesis\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Imperial College Press","offers":[{"title":"Default Title","offer_id":47136900907248,"sku":"9781783263042","price":34.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9781783263042_p0.jpg?v=1763723857","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9781783263042","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}