# Some approximation problems in semi-algebraic geometry

Shmuel Friedland; Małgorzata Stawiska

Banach Center Publications (2015)

- Volume: 107, Issue: 1, page 133-147
- ISSN: 0137-6934

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topShmuel 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 -

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