Univariate Lp and ɭ p Averaging, 0 < p < 1, in Polynomial Time by Utilization of Statistical Structure
نویسندگان
چکیده
منابع مشابه
Convex Polynomial and Spline Approximation in Lp , 0 < p <
We prove that a convex function f 6 L p [ -1 , 1], 0 < p < cx~, can be approximated by convex polynomials with an error not exceeding Cw~ (f, 1/n)p where w~(f, .) is the Ditzian-Totik modulus of smoothness of order three of f . We are thus filling the gap between previously known estimates involving og~(f, I/n)p, and the impossibility of having such estimates involving ~o4. We also give similar...
متن کاملPolynomial Approximation in Lt , ( 0 < p < 1 )
We are interested in the approximation of functions f ~ Lp(I), 0 < p < 1, I = [ 1 , 1], by algebraic polynomials. Such approximation has previously been studied by other authors, most notably, Storozhenko, Krotov, and Oswald [-S-K-O] and Khodak [K]. Our main departure from these previous works is that we shall prove direct estimates for the error of polynomial approximation in terms of the Ditz...
متن کاملLp-Regularized Least Squares (0<p<1) and Critical Path
The least squares problem is formulated in terms of lp quasi-norm regularization (0 < p < 1). Two formulations are considered: (i) an lp-constrained optimization and (ii) an lp-penalized (unconstrained) optimization. Due to the nonconvexity of the lp quasi-norm, the solution paths of the regularized least squares problem are not ensured to be continuous. A critical path, which is a maximal cont...
متن کاملA NOTE ON THE SPACES Lp FOR 0 < p < 1
It is shown that there is no Hausdorff vector topology p on the space Lp (where 0 < p < 1) such that the unit ball of Lp is relatively compact for the topology p. It is well known that the space L1 (0, 1) is not a dual Banach space; this follows from the Krein-Milman theorem. It is not even isomorphic to a dual space, by a result due to Gelfand [2] (see Bessaga and Pelczyn'ski [1] and Namioka [...
متن کاملAffine Synthesis onto Lp when 0 < p ≤ 1
The affine synthesis operator Sc = ∑j>0 ∑k∈Zd cj,kψj,k is shown to map the coefficient space (Z+ × Zd ) surjectively onto Lp(Rd ), for p ∈ (0, 1]. Here ψj,k(x) = | det aj |ψ(aj x − k) for dilation matrices aj that expand, and the synthesizer ψ ∈ Lp(Rd ) need satisfy only mild restrictions, for example, ψ ∈ L1(Rd ) with nonzero integral or else with periodization that is real-valued, nontrivial ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algorithms
سال: 2012
ISSN: 1999-4893
DOI: 10.3390/a5040421