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Chebyshev projection in non-symmetrical polyhedral spacesтезисы доклада
- Автор: Tsar'kov I.G.
- Сборник: Abstracts. International conference “High-dimensional approximation and discretization
- Тезисы
- Год издания: 2018
- Место издания: Laboratory of high-dimensional approximation and applications Moscow
- Первая страница: 17
- Последняя страница: 18
- Аннотация: \textbf{Theorem~1.} {\it Let $(X,\|\cdot|)$ be a non-symmetrical finite dimensional polyhedral space and let $V\subset X$ be a nonempty linear polyhedral set. Then there exist a number $c=c(V)>0$ that for any bounded sets $M,N\subset X$ the estimate $h(Z_V(M),Z_V(N))\leqslant ch( M, N )$ holds and there exist a single-valued Lipschitz map $M\stackrel{\varphi}{\rightarrow}Z_V(M)$ $($i.e. a selection from the operator $Z_V(\cdot))$ which corresponds any bounded set to a its relative Chebyshev center.
- Добавил в систему: Царьков Игорь Германович