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Artificial neural networks with uniform norm-based loss functions
We explore the potential for using a nonsmooth loss function based on the max-norm in the training of an artificial neural network without hidden...
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Approximation of curve-based sleeve functions in high dimensions
Sleeve functions are generalizations of the well-established ridge functions that play a major role in the theory of partial differential equation,...
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Learning via variably scaled kernels
We investigate the use of the so-called variably scaled kernels (VSKs) for learning tasks, with a particular focus on support vector machine (SVM)...
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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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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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Variational Monte Carlo—bridging concepts of machine learning and high-dimensional partial differential equations
A statistical learning approach for high-dimensional parametric PDEs related to uncertainty quantification is derived. The method is based on the...
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Nonlinear stationary subdivision schemes reproducing hyperbolic and trigonometric functions
In this paper we introduce a new family of interpolatory subdivision schemes with the capability of reproducing trigonometric and hyperbolic...
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Factorization of Hermite subdivision operators preserving exponentials and polynomials
In this paper we focus on Hermite subdivision operators that act on vector valued data interpreting their components as function values and...
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Analog to Digital, Revisited: Controlling the Accuracy of Reconstruction
In this work, we study analog-to-digital conversion and reconstruction outside of the strict régime of the sampling theorem for band-limited...
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Reconstruction of Piecewise Smooth Functions from Non-uniform Grid Point Data
Spectral series expansions of piecewise smooth functions are known to yield poor results, with spurious oscillations forming near the jump...
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Modified Sinc Kernels for the Localized Sampling Series
We propose generalized sinc kernels for the localized sampling series, derive explicit error estimates for the sampling series to approximate a...
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On a diagonal Padé approximation in two complex variables
A special type diagonal Padé approximation for a class of hermitian power series in two variables is related to a canonical strong-operator topology,...
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An extension of A. Ostrowski's Theorem on the round-off stability of iterations
A. M. Ostrowski established the stability of the procedure of successive approximations for Banach contractive maps. In this paper we generalize the...
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Asymptotic expansion and extrapolation for Bernstein polynomials with applications
Given a real function f ε C 2 k [0,1], k ≥ 1 and the corresponding Bernstein polynomials { B n ( f )} n we derive an asymptotic expansion formula for B ...
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Analytic wavelets generated by radial functions
In this paper, we deal with a class of non-stationary multiresolution analysis and wavelets generated by certain radial basis functions. These radial...
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Chebyshev approximation by discrete superposition. Application to neural networks
In this paper, we develop two algorithms for Chebyshev approximation of continuous functions on [0, 1] n using the modulus of continuity and the...
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An algorithm for chebyshev approximation by rationals with constrained denominators
The problem of rational approximation is facilitated by introducing both lower and upper bounds on the denominators. For a general fractional inf-sup...
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P
A group which has a normal series such that the order of every factor contains at most one prime from π (π is a set of prime numbers). The class of...