✦ LIBER ✦
Asymptotic Behaviour of Best lp-Approximations from Affi ne Subspaces
✍ Scribed by J.M. Quesada; J. Martinez-Moreno; J. Navas
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 158 KB
- Volume
- 118
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
✦ Synopsis
In this paper we consider the problem of best approximation in ' n p ; 15p41: If h p ; 15p51; denotes the best ' p -approximation of the element h 2 R n from a proper affine subspace
where h n 1 is a best uniform approximation of h from K; the so-called strict uniform approximation. Our aim is to prove that for all r 2 N there are a j 2 R n ; 14j4r; such that
g ðrÞ p ; with g ðrÞ p 2 R n and jjg ðrÞ p jj ¼ Oðp ÀrÀ1 Þ: # 2002 Elsevier Science (USA)