We consider the classical problem of finding the best uniform approximation by polynomials of 1/(x − a), where a > 1 is given, on the interval [−1, 1]. First, using symbolic computation tools we derive the explicit expressions of the polynomials of best approximation of low degrees and then give a parametric solution of the problem in terms of elliptic functions. Symbolic computation is invoked...

Abstract. We consider 3-monotone approximation by piecewise polynomials with prescribed knots. A general theorem is proved, which reduces the problem of 3-monotone uniform approximation of a 3-monotone function, to convex local L1 approximation of the derivative of the function. As the corollary we obtain Jackson-type estimates on the degree of 3-monotone approximation by piecewise polynomials ...

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 ,∞}. ...

In this paper we present an RNC-algorithm for nding a minimum spanning tree in a weighted 3-uniform hypergraph, assuming the edge weights are given in unary, and a fully polynomial time randomized approximation scheme if the edge weights are given in binary. From this result we then derive RNC-approximation algorithms for the Steiner problem in networks with approximation ratio (1 +) 5=3 for al...

We derive L 1 bounds for norms of projections onto bivariate polynomial spline spaces on regular triangulations with stable local bases. We then apply this result to derive error bounds for best L 2-and`2-approximation by splines on quasi-uniform triangulations. x1. Introduction Let X L 1 (() be a linear space deened a set with polygonal boundary. Suppose hh; i is a semi-deenite inner-product o...

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.