We analyze the accuracy of the discrete least-squares approximation of a function u in multivariate polynomial spaces PΛ := span{y 7→ y : ν ∈ Λ} with Λ ⊂ N0 over the domain Γ := [−1, 1], based on the sampling of this function at points y, . . . , y ∈ Γ. The samples are independently drawn according to a given probability density ρ belonging to the class of multivariate beta densities, which inc...

A product quadrature rule, based on the filtered de la Vallée Poussin polynomial approximation, is proposed for evaluating finite weighted Hilbert transform in [ − 1 , ] . Convergence results are stated uniform norm functions belonging to suitable Besov type subspaces. Several numerical tests provided, also comparing rule with other formulas known literature.

we obtain a sucint and nesessery theoreoms simple for compactness andweakly compactness of the best approximate sets by closed unit balls. also weconsider relations kadec-klee property and shur property with this objects.these theorems are extend of papers mohebi and narayana.

In this paper, we study tractability of L2-approximation one-periodic functions from weighted Korobov spaces in the worst-case setting. The considered weights are product form. For algorithms allow information class ?all consisting all continuous linear functionals and ?std, which only consists function evaluations. We provide necessary sufficient conditions on space for quasi-polynomial tracta...

In a recent paper, Chekuri and Bender (Proceedings of IPCO’98, pp. 383–393) derive (among other results) a polynomial-time 6-approximation algorithm for makespan minimization on uniform parallel machines subject to chain-type precedence constraints. In this short note, we combine some straightforward observations and thereby derive an extremely simple 2-approximation algorithm for this problem....

We study the problem of revenue maximization in the marketing model for social networks introduced by (Hartline, Mirrokni, Sundararajan, WWW ’08). In this setting, a digital product is sold to a set of potential buyers under positive externalities, and the seller seeks for a marketing strategy, namely an ordering in which he approaches the buyers and the prices offered to them, that maximizes h...