Tractability of Multivariate Approximation Defined over Hilbert Spaces\n with Exponential Weights

2015/02/11 by Christian Irrgeher, Peter Kritzer, Irrgeher, Christian +5
Engineering · Mathematics · #41A25 #41A63 #65D15 #65Y20 #Advanced Numerical Analysis Techniques #Approximation Theory and Sequence Spaces #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1502.03286

openalex publication_date 2015/02/11 · openalex created_date 2022/10/06 · openalex updated_date 2026/08/01

Abstract

We study multivariate approximation defined over tensor product Hilbert\nspaces. The domain space is a weighted tensor product Hilbert space with\nexponential weights which depend on two sequences\n boldsymbola= a_{j j\∈\ℕ} and\n boldsymbolb= b_{j j\∈\ℕ} of positive numbers, and on a bounded\nsequence of positive integers boldsymbolm= m_{j j\∈\ℕ}. The\nsequence boldsymbola is non-decreasing and the sequence boldsymbolb\nis bounded from below by a positive number. We find necessary and sufficient\nconditions on boldsymbola, boldsymbolb and boldsymbolm to achieve\nthe standard and new notions of tractability in the worst case setting.\n

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