Some approximation problems in semi-algebraic geometry

Shmuel Friedland, and Małgorzata Stawiska. "Some approximation problems in semi-algebraic geometry." Banach Center Publications 107.1 (2015): 133-147. <http://eudml.org/doc/282045>.

@article{ShmuelFriedland2015,
abstract = {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).},
author = {Shmuel Friedland, Małgorzata Stawiska},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {133-147},
title = {Some approximation problems in semi-algebraic geometry},
url = {http://eudml.org/doc/282045},
volume = {107},
year = {2015},
}

TY - JOUR
AU - Shmuel Friedland
AU - Małgorzata Stawiska
TI - Some approximation problems in semi-algebraic geometry
JO - Banach Center Publications
PY - 2015
VL - 107
IS - 1
SP - 133
EP - 147
AB - 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).
LA - eng
UR - http://eudml.org/doc/282045
ER -