Best approximation by ridge functions in L p -spaces

Some Results on p-Best Approximation in Vector Spaces

BEST SIMULTANEOUS APPROXIMATION IN FUZZY NORMED SPACES

The main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. We develop the theory of t-bestsimultaneous approximation in quotient spaces. Then, we discuss the relationshipin t-proximinality and t-Chebyshevity of a given space and its quotientspace.

t-BEST APPROXIMATION IN FUZZY NORMED SPACES

The main purpose of this paper is to find t-best approximations in fuzzy normed spaces. We introduce the notions of t-proximinal sets and F-approximations and prove some interesting theorems. In particular, we investigate the set of all t-best approximations to an element from a set.

some results on p-best approximation in vector spaces

Approximation by Ridge Functions and Neural Networks

We investigate the efficiency of approximation by linear combinations of ridge functions in the metric of L2(B ) with Bd the unit ball in Rd. If Xn is an n-dimensional linear space of univariate functions in L2(I), I = [−1, 1], and Ω is a subset of the unit sphere Sd−1 in Rd of cardinality m, then the space Yn := span{r(x · ξ) : r ∈ Xn, ω ∈ Ω} is a linear space of ridge functions of dimension ≤...