Some approximation problems in semi-algebraic geometry

• Autorzy: Shmuel Friedland , Małgorzata Stawiska
• Języki publikacji: EN

Abstrakty

EN

In this paper we deal with a best approximation of a vector with respect to a closed semi-algebraic set C in the space ℝⁿ endowed with a semi-algebraic norm ν. Under additional assumptions on ν we prove semi-algebraicity of the set of points of unique approximation and other sets associated with the distance to C. For C irreducible algebraic we study the critical point correspondence and introduce the ν-distance degree, generalizing the notion developed by other authors for the Euclidean norm. We discuss separately the case of the $ℓ^p$ norm (p > 1).

Kategorie tematyczne

• 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
• 41A52: Uniqueness of best approximation
• 14P10: Semialgebraic sets and related spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2015
• Tom: 107
• Numer: 1
• Strony: 133-147

Daty

wydano

2015

Twórcy

autor

Shmuel Friedland

• Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607-7045, USA

autor

Małgorzata Stawiska

• Mathematical Reviews, 416 Fourth Street, Ann Arbor, MI 48103-4816, USA

Identyfikatory

DOI

10.4064/bc107-0-9