Approximation by multivariate max-product Kantorovich-type operators and learning rates of least-squares regularized regression. (English) Zbl 1472.41011
In a recent paper, for univariate max-product sampling operators based on general kernels with bounded generalized absolute moments, the authors have obtained several \(L_\mu^p\) convergence properties on bounded intervals or on the whole real axis. In this paper, firstly the authors obtain quantitative estimates with respect to a K-functional, for the multivariate Kantorovich variant of these max-product sampling operators with the integrals written in terms of Borel probability measures. Applications of these approximation results to learning theory are obtained
Reviewer: Vijay Gupta (New Delhi)
MSC:
| 41A35 | Approximation by operators (in particular, by integral operators) |
| 41A25 | Rate of convergence, degree of approximation |
| 41A63 | Multidimensional problems |
Keywords:
multivariate max-product; sampling Kantorovich operators; Borel probability measures; multivariate generalized kernels; K-functional; learning theory; regularizing function; sample error; regularized errorReferences:
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