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Explicit RIP matrices: an update
Leveraging recent advances in additive combinatorics, we exhibit explicit matrices satisfying the Restricted Isometry Property with better...
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Trotter-Kato Approximations of Impulsive Neutral SPDEs in Hilbert Spaces
This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces. The main goal here is to consider...
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Optimal Birkhoff Interpolation and Birkhoff Numbers in Some Function Spaces
This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L ∞ [−1, 1] and weighted spaces L p,ω [−1...
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Linear/Ridge expansions: enhancing linear approximations by ridge functions
We consider approximations formed by the sum of a linear combination of given functions enhanced by ridge functions—a Linear/Ridge expansion. For an...
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Nuclear and Compact Embeddings in Function Spaces of Generalised Smoothness
We study nuclear embeddings for function spaces of generalised smoothness defined on a bounded Lipschitz domain Ω ⊂ ℝ d . This covers, in particular,...
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Pairwise ranking with Gaussian kernel
Regularized pairwise ranking with Gaussian kernels is one of the cutting-edge learning algorithms. Despite a wide range of applications, a rigorous...
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Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs
We demonstrate that deep neural networks with the ReLU activation function can efficiently approximate the solutions of various types of parametric...
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Tensor rank bounds for point singularities in ℝ3
We analyze rates of approximation by quantized, tensor-structured representations of functions with isolated point singularities in ℝ 3 . We consider...
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Convergence to Zero of Exponential Sums with Positive Integer Coefficients and Approximation by Sums of Shifts of a Single Function on the Line
We prove that there is a sequence of trigonometric polynomials with positive integer coefficients, which converges to zero almost everywhere. We also...
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The best m-term approximation with respect to polynomials with constant coefficients
In this paper we show that greedy bases can be defined as those where the error term using m -greedy approximant is uniformly bounded by the best m -ter...
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Nonlinear wavelet approximation of periodic function classes with generalized mixed smoothnes
We study the approximation properties of L q -greedy algorithms with respect to the known wavelet type system U d , which consists of shifts of the...
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Optimal sampling recovery of mixed order Sobolev embeddings via discrete Littlewood–Paley type characterizations
In this paper we consider the L q -approximation of multivariate periodic functions f with L q -bounded mixed derivative (difference). The (possibly...
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Dictionary descent in optimization
The problem of convex optimization is studied. Usually in convex optimization the minimization is over a d -dimensional domain. Very often the...
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On a problem of Hornik
In 1991, Hornik proved that the collection of single hidden layer feedforward neural networks (SLFNs) with continuous, bounded, and non-constant...
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Approximation of eigenfunctions in kernel-based spaces
Kernel-based methods in Numerical Analysis have the advantage of yielding optimal recovery processes in the “native” Hilbert space
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On n-widths of a Sobolev function class in Orlicz spaces
This paper considers the problem of n -widths of a Sobolev function class Ω
∞ r determined by P r ( D ) = D σ Πj =1 l ( D 2 − t ... -
Efficiency of weak greedy algorithms for m-term approximations
We investigate the efficiency of weak greedy algorithms for m-term expansional approximation with respect to quasi-greedy bases in general Banach...