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Approximation Properties of the Double Fourier Sphere Method
We investigate analytic properties of the double Fourier sphere (DFS) method, which transforms a function defined on the two-dimensional sphere to a...
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Fast hyperbolic wavelet regression meets ANOVA
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions....
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A deterministic algorithm for constructing multiple rank-1 lattices of near-optimal size
In this paper we present the first known deterministic algorithm for the construction of multiple rank-1 lattices for the approximation of periodic...
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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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Strong Equivalences of Approximation Numbers and Tractability of Weighted Anisotropic Sobolev Embeddings
In this article, we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a = { a j } j ≥1 and b ...
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On Universal Sampling Recovery in the Uniform Norm
AbstractIt is known that results on universal sampling discretization of the square norm are useful in sparse sampling recovery with error measured...
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High-Dimensional FFT
In this chapter, we discuss methods for the approximation of d-variate functions in high-dimension...
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Frame approximation with bounded coefficients
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a...
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Classes of Functions
In this chapter, we briefly present well-known classes of functions that will play an important role in our considerations. Of course, the list of...
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Estimates for the Deviations of Integral Operators in Semilinear Metric Spaces and Their Applications
We develop the theory of approximations in functional semilinear metric spaces that allows us to consider the classes of multi- and fuzzy-valued...
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Nonuniform sampling and approximation in Sobolev space from perturbation of the framelet system
The Sobolev space H ς (ℝ d ), where ς > d /2, is an important function space that has many applications in various areas of research. Attributed to the...
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On the Approximation of Functions by Polynomials and Entire Functions of Exponential Type
We present a brief survey of works in the approximation theory of functions known to the author and connected with V. K. Dzyadyk’s research works.
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Sparse harmonic transforms II: best s-term approximation guarantees for bounded orthonormal product bases in sublinear-time
In this paper we develop a sublinear-time compressive sensing algorithm for approximating functions of many variables which are compressible in a...
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Sufficient Conditions for a Multidimensional System of Periodic Wavelets to be a Frame
We study multidimensional periodic wavelet systems with matrix dilations. We obtain conditions sufficient for such a system to be Bessel. The...
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Numerical Applications of DFT
This chapter addresses numerical applications of DFTs. In Sect. 9.1, we describe a powerful multidimensional approximation method, the so-called...