Applications of classical approximation theory to periodic basis function networks and computational harmonic analysis

DOI10.1007/s13373-013-0043-1zbMath1281.93110OpenAlexW2038553817WikidataQ59305029 ScholiaQ59305029MaRDI QIDQ5396581

Eugene Shvarts, Paul G. Nevai, Hrushikesh N. Mhaskar

Publication date: 31 January 2014

Published in: Bulletin of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13373-013-0043-1

zbMATH Keywords

trigonometric polynomialsapproximation theoryperiodic basis function networksperiodic univariate and multivariate functions

Mathematics Subject Classification ID

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Cites Work

• Optimally space localized polynomials with applications in signal processing
• On the problem of parameter estimation in exponential sums
• Minimum Sobolev norm interpolation with trigonometric polynomials on the torus
• Interpolation of scattered data: distance matrices and conditionally positive definite functions
• Theory and applications of the multiquadric-biharmonic method. 20 years of discovery 1968-1988
• Marcinkiewicz-Zygmund measures on manifolds
• Density estimation through convex combinations of densities: Approximation and estimation bounds
• Quadrature formulas for integration of multivariate trigonometric polynomials on spherical triangles
• Polynomial operators and local smoothness classes on the unit interval
• s-numbers in information-based complexity
• On local smoothness classes of periodic functions
• Eignets for function approximation on manifolds
• On a filter for exponentially localized kernels based on Jacobi polynomials
• Mean convergence of Lagrange interpolation. I
• Norm estimates for the inverses of a general class of scattered-data radial-function interpolation matrices
• Approximation by superposition of sigmoidal and radial basis functions
• Orthogonal algebraic polynomial Schauder bases of optimal degree
• On the representation of smooth functions on the sphere using finitely many bits
• Optimal nonlinear approximation
• When is approximation by Gaussian networks necessarily a linear process?
• Local quadrature formulas on the sphere
• Degree of approximation by neural and translation networks with a single hidden layer
• Orthogonal trigonometric Schauder bases of optimal degree for \(C(K)\)
• A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel
• Approximation properties of zonal function networks using scattered data on the sphere
• On the detection of singularities of a periodic function
• Multivariate approximation by translates of the Korobov function on Smolyak grids
• Positive cubature formulas and Marcinkiewicz-Zygmund inequalities on spherical caps
• Almost optimal estimates for best approximation by translates on a torus
• Diffusion polynomial frames on metric measure spaces
• Polynomial operators for spectral approximation of piecewise analytic functions
• Spherical harmonics
• On convergence and growth of partial sums of Fourier series
• Über die Approximationsordnung bei Kugelfunktionen und algebraischen Polynomen
• Norms of inverses and condition numbers for matrices associated with scattered data
• Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature
• Inverse and saturation theorems for radial basis function interpolation
• Smooth function extension based on high dimensional unstructured data
• $L^p$ Bernstein estimates and approximation by spherical basis functions
• Matrix Analysis
• Dimension-independent bounds on the degree of approximation by neural networks
• Decision region approximation by polynomials or neural networks
• Orthonormal Polynomial Wavelets on the Interval and Applications to the Analysis of Turbulent Flow Fields
• Localized Linear Polynomial Operators and Quadrature Formulas on the Sphere
• Nearly optimal sparse fourier transform
• A Convolution Structure for Jacobi Series
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