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Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed: one uses the contour integral representation and conformal mapping, and the other is based on a versi...
Let us consider a Riemannian manifold M (either separable or non-separable). We prove that, for every " > 0, every Lipschitz function f : M ! R can be uniformly approximated by a Lipschitz, C1-smooth ...
In this paper we consider first order differential models of collective behaviors of groups of agents based on the mass conservation equation. Models are formulated taking the spatial distribution o...
We prove that the size of the sparsest directed k-spanner of a graph can be approximated in polynomial time to within a factor of ˜O(√n), for all k ≥ 3. This improves the ˜O(n2/3)- approxim...
Given a nonnegative polynomial f, we provide an explicit expres-sion for its best ℓ1-norm approximation by a sum of squares of given degree.
Functions satisfying a defective renewal equation arise commonly in applied probability models. Usually these functions don’t admit a explicit expression. In this work we consider to approximate them ...
Weighted low-rank approximation (WLRA), a dimensionality reduction technique for data anal- ysis, has been successfully used in several applications, such as in collaborative filtering to design reco...
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting.
The frozen Gaussian approximation provides a highly efficient computational method for high frequency wave propagation. The derivation of the method is based on asymptotic analysis. In this paper, fo...
Let X be a separable Banach space which admits a separating polynomial; in particular X a separable Hilbert space. Let $f:X \rightarrow R$ be bounded, Lipschitz, and $C^1$ with uniformly continuous d...
In this paper we study the spectrum of long-range percolation graphs. The underlying geometry is given in terms of a finitely generated amenable group. We prove that the integrated density of states (...
We introduce the concept of average best m-term approximation widths with respect to a probability measure on the unit ball of ℓnp .
This is an expository paper on approximating functions from general Hilbert or Banach spaces in the worst case, average case and randomized settings with error measured in the $L_p$ sense. We define ...
We obtain an analog of Shvedov theorem for convex multivariate approximation by algebras of continuous functions.
We analyse the exponential stability properties of a class of measure-valued equations arising in nonlinear multi-target filtering problems. We also prove the uniform convergence properties w.r.t. the...

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