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Uniqueness of solutions in multivariate Chebyshev approximation problems
We study the solution set to multivariate Chebyshev approximation problem, focussing on the ill-posed case when the uniqueness of solutions can not...
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New Lower Bounds for the Integration of Periodic Functions
We study the integration problem on Hilbert spaces of (multivariate) periodic functions.The standard technique to prove lower bounds for the error of...
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Constructing Embedded Lattice-Based Algorithms for Multivariate Function Approximation with a Composite Number of Points
We approximate d -variate periodic functions in weighted Korobov spaces with general weight parameters using n function values at lattice points. We...
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Kolmogorov Widths of the Nikol’skii–Besov Classes of Periodic Functions of Many Variables in the Space of Quasicontinuous Functions
We obtain order estimates for the M -dimensional Kolmogorov widths of the Nikol’skii–Besov classes of periodic functions of many variables with...
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Variable transformations in combination with wavelets and ANOVA for high-dimensional approximation
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low-dimensional variable interactions....
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Characteristics of the linear and nonlinear approximations of the Nikol’skii–Besov-type classes of periodic functions of several variables
Estimates that are accurate by order of magnitude have been obtained for some characteristics of the linear and nonlinear approximations of the...
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Approximation characteristics of the Nikol’sky-Besov-type classes of periodic single- and multivariable functions in the B1,1 space
Exact order-of-magnitude estimates of the orthowidths and similar to them approximate characteristics of the Nikol’sky-Besov-type classes of periodic...
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Best Orthogonal Trigonometric Approximations of the Nikol’skii–Besov-Type Classes of Periodic Functions in the Space B∞,1
Exact-order estimates are obtained for the best orthogonal trigonometric approximations of the Nikol’skii–Besov-type classes of periodic functions of...
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Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification
This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice—a...
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Approximation in the extended functional tensor train format
This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product...
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Sparse Grid Approximation in Weighted Wiener Spaces
We study approximation properties of multivariate periodic functions from weighted Wiener spaces by sparse grid methods constructed with the help of...
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Discrete Periodic Multiresolution Analysis
Periodic multiresolution analyses in the space of periodic complex-valued functions of an integer argument are studied. A characterization of...
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Multivariate quasi-tight framelets with high balancing orders derived from any compactly supported refinable vector functions
Generalizing wavelets by adding desired redundancy and flexibility, framelets (i.e., wavelet frames) are of interest and importance in many...
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Analysis of Tensor Approximation Schemes for Continuous Functions
In this article, we analyze tensor approximation schemes for continuous functions. We assume that the function to be approximated lies in an...
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Sharp Constants of Approximation Theory. IV. Asymptotic Relations in General Settings
In this paper we first introduce the unified definition of the sharp constant that includes constants in three major problems of approximation...
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Uncertainty quantification for random domains using periodic random variables
We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random...
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Nonlinear approximation in bounded orthonormal product bases
We present a dimension-incremental algorithm for the nonlinear approximation of high-dimensional functions in an arbitrary bounded orthonormal...
