Approximation by multivariate Bernstein-Durrmeyer operators and learning rates of least-squares regularized regression with multivariate polynomial kernels

DOI10.1016/j.jat.2013.04.007zbMath1282.41009OpenAlexW2064538010MaRDI QIDQ390534

Bing-Zheng Li

Publication date: 8 January 2014

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2013.04.007

zbMATH Keywords

learning theoryapproximationcovering numberreproducing kernel Hilbert spacepolynomial kernelregularization schemeBernstein-Durrmayer operatorsregularization error

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Multidimensional problems (41A63) Approximation by positive operators (41A36)

Related Items (16)

The kernel regularized learning algorithm for solving Laplace equation with Dirichlet boundary ⋮ Approximation on variable exponent spaces by linear integral operators ⋮ Error analysis on regularized regression based on the maximum correntropy criterion ⋮ Quantitative estimates in \(L^{p}\)-approximation by Bernstein-Durrmeyer-Choquet operators with respect to distorted Borel measures ⋮ Approximation by multivariate max-product Kantorovich-type operators and learning rates of least-squares regularized regression ⋮ Approximation by multivariate Baskakov-Durrmeyer operators in Orlicz spaces ⋮ Quantitative Estimates for $L^p$-Approximation by Bernstein-Kantorovich-Choquet Polynomials with Respect to Distorted Lebesgue Measures ⋮ Analysis of approximation by linear operators on variable \(L_\rho^{p(\cdot)}\) spaces and applications in learning theory ⋮ Uniform and pointwise convergence of Bernstein-Durrmeyer operators with respect to monotone and submodular set functions ⋮ Bernstein-Durrmeyer operators with respect to arbitrary measure. II: Pointwise convergence ⋮ Multivariate Bernstein operators and redundant systems ⋮ Operators of Durrmeyer Type with Respect to Arbitrary Measure ⋮ Pointwise convergence of the Bernstein-Durrmeyer operators with respect to a collection of measures ⋮ The learning rates of regularized regression based on reproducing kernel Banach spaces ⋮ Approximation by max-product operators of Kantorovich type ⋮ Approximation by max-product sampling Kantorovich operators with generalized kernels

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