Solotaree's approximation problem is that of obtaining the best uniform approximation on the interval-1,+1] of a real polynomial of degree n by one of degree n ? 2 or less. Without loss of generalitywe take the approximated polynomial to be x n +rx n?1 , r 0. We treat r as a parameter and seek to compute the coeecients of the best approximations, for small xed values of n, as piecewise algebrai...

In this paper we obtain the explicit form of the best uniform polynomial approximations out of Pn of two classes of rational functions using properties of Chebyshev polynomials. In this way we present some new theorems and lemmas. Some examples will be given to support the theoretical results.

The authors consider the generalized airfoil equation in some weighted Hölder–Zygmund spaces with uniform norms. Using a projection method based on the de la Vallée Poussin interpolation, they find an approximate polynomial solution which converges to the original solution like the best uniform weighted polynomial approximation. The proposed numerical procedure leads to solve a tridiagonal line...

For each q ∈ N0, we construct positive linear polynomial approximation operators Mn that simultaneously preserve k-monotonicity for all 0 ≤ k ≤ q and yield the estimate |f(x)−Mn(f, x)| ≤ cω λ 2 ( f, nφ(x) (φ(x) + 1/n) ) , for x ∈ [0, 1] and λ ∈ [0, 2), where φ(x) := √ x(1− x) and ω 2 is the second Ditzian-Totik modulus of smoothness corresponding to the “step-weight function” ψ. In particular, ...

In this paper, we present an efficient polynomial time approximation scheme (EPTAS) for scheduling on uniform processors, i.e. finding a minimum length schedule for a set of n independent jobs on m processors with different speeds (a fundamental NP-hard scheduling problem). The previous best polynomial time approximation scheme (PTAS) by Hochbaum and Shmoys has a running time of (n/ ) 2). Our a...