We derive a three-term recurrence relation for computing the polynomial of best approximation in the uniform norm to x−1 on a finite interval with positive endpoints. As application, we consider two-level methods for scalar elliptic partial differential equation (PDE), where the relaxation on the fine grid uses the aforementioned polynomial of best approximation. Based on a new smoothing proper...

Scheduling jobs on unrelated machines and minimizing the makespan is a classical problem in combinatorial optimization. In this problem a job j has a processing time pij for every machine i. The best polynomial algorithm known goes back to Lenstra et al. and has an approximation ratio of 2. In this paper we study the Restricted Assignment problem, which is the special case where pij ∈ {pj ,∞}. ...

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.

We present a polynomial time algorithm for the unit disk covering problem with an approximation factor 72, and show that this is the best possible approximation factor based on the method used. This is an improvement on the best known approximation factor of 108.

We present a polynomial-time approximation algorithm for legally coloring as many edges of a given simple graph as possible using two colors. It achieves an approximation ratio of roughly 0.842 and runs in O(nm) time, where n (respectively, m) is the number of vertices (respectively, edges) in the input graph. The previously best ratio achieved by a polynomial-time approximation algorithm was 5...

In this paper, the problem of best uniform polynomial approximation to a continuous function on a compact set X is approached through the partitioning of X and the definition of norms corresponding to the partition and each of the standard Lp norms 1 g p < oo. For computational convenience, a pseudo norm is defined corresponding to each partition. When the partition is chosen appropriately, the...

Given a graph G = (V,E) with node weight w : V → R and a subset S ⊆ V , find a minimum total weight tree interconnecting all nodes in S. This is the node-weighted Steiner tree problem which will be studied in this paper. In general, this problem is NP-hard and cannot be approximated by a polynomial time algorithm with performance ratio a lnn for any 0 < a < 1 unless NP ⊆ DTIME(n), where n is th...